diff --git a/docs/src/CommutativeAlgebra/rings.md b/docs/src/CommutativeAlgebra/rings.md
index aa09ec1d811b..d9ea584c43b9 100644
--- a/docs/src/CommutativeAlgebra/rings.md
+++ b/docs/src/CommutativeAlgebra/rings.md
@@ -405,7 +405,7 @@ julia> R, (x, y) = polynomial_ring(QQ, ["x", "y"])
 (Multivariate polynomial ring in 2 variables over QQ, QQMPolyRingElem[x, y])
 
 julia> B = MPolyBuildCtx(R)
-Builder for an element of Multivariate polynomial ring in 2 variables over QQ
+Builder for an element of multivariate polynomial ring
 
 julia> for i = 1:5 push_term!(B, QQ(i), [i, i-1]) end
 
diff --git a/docs/src/NumberTheory/galois.md b/docs/src/NumberTheory/galois.md
index 9294ab41c1b8..0d878cbbd3f8 100644
--- a/docs/src/NumberTheory/galois.md
+++ b/docs/src/NumberTheory/galois.md
@@ -96,10 +96,10 @@ julia> F, a = function_field(x^6 + 108*t^2 + 108*t + 27);
 
 julia> subfields(F)
 4-element Vector{Any}:
- (Function Field over Rational field with defining polynomial a^3 + 54*t + 27, (1//12*_a^4 + (3//2*t + 3//4)*_a)//(t + 1//2))
- (Function Field over Rational field with defining polynomial a^2 + 108*t^2 + 108*t + 27, _a^3)
- (Function Field over Rational field with defining polynomial a^3 - 108*t^2 - 108*t - 27, -_a^2)
- (Function Field over Rational field with defining polynomial a^3 - 54*t - 27, (-1//12*_a^4 + (3//2*t + 3//4)*_a)//(t + 1//2))
+ (Function Field over QQ with defining polynomial a^3 + 54*t + 27, (1//12*_a^4 + (3//2*t + 3//4)*_a)//(t + 1//2))
+ (Function Field over QQ with defining polynomial a^2 + 108*t^2 + 108*t + 27, _a^3)
+ (Function Field over QQ with defining polynomial a^3 - 108*t^2 - 108*t - 27, -_a^2)
+ (Function Field over QQ with defining polynomial a^3 - 54*t - 27, (-1//12*_a^4 + (3//2*t + 3//4)*_a)//(t + 1//2))
 
 julia> galois_group(F)
 (Permutation group of degree 6 and order 6, Galois context for s^6 + 108*t^2 + 540*t + 675)
diff --git a/experimental/ModStd/src/ModStdQt.jl b/experimental/ModStd/src/ModStdQt.jl
index b4268bc519bd..20f36b48a9e1 100644
--- a/experimental/ModStd/src/ModStdQt.jl
+++ b/experimental/ModStd/src/ModStdQt.jl
@@ -591,7 +591,7 @@ julia> f = factor_absolute((X[1]^2+a[1]*X[2]^2)*(X[1]+2*X[2]+3*a[1]+4*a[2]))
 
 julia> parent(f[3][1])
 Multivariate polynomial ring in 2 variables X[1], X[2]
-  over fraction field of multivariate polynomial ring
+  over fraction field of Qa
 
 julia> parent(f[2][1])
 Multivariate polynomial ring in 2 variables X[1], X[2]
diff --git a/experimental/Schemes/CoveredProjectiveSchemes.jl b/experimental/Schemes/CoveredProjectiveSchemes.jl
index 4a17ec3edcf3..6b56b606d78d 100644
--- a/experimental/Schemes/CoveredProjectiveSchemes.jl
+++ b/experimental/Schemes/CoveredProjectiveSchemes.jl
@@ -311,7 +311,7 @@ julia> R, (x,y,z) = QQ["x", "y", "z"];
 
 julia> Oscar.empty_covered_projective_scheme(R)
 Relative projective scheme
-  over empty covered scheme over multivariate polynomial ring
+  over empty covered scheme over R
 covered with 0 projective patches
 ```
 """
diff --git a/experimental/Schemes/duValSing.jl b/experimental/Schemes/duValSing.jl
index 5838df813b9e..fa6b7bb4d9d5 100644
--- a/experimental/Schemes/duValSing.jl
+++ b/experimental/Schemes/duValSing.jl
@@ -14,7 +14,7 @@ Ideal generated by
   x^2 + y^3 + z^4
 
 julia> Rq, _ = quo(R,I)
-(Quotient of multivariate polynomial ring by ideal (w, x^2 + y^3 + z^4), Map: multivariate polynomial ring -> Rq)
+(Quotient of multivariate polynomial ring by ideal (w, x^2 + y^3 + z^4), Map: R -> Rq)
 
 julia> X = spec(Rq)
 Spectrum
@@ -78,7 +78,7 @@ Ideal generated by
   x^2 + y^3 + z^4
 
 julia> Rq, _ = quo(R,I)
-(Quotient of multivariate polynomial ring by ideal (w, x^2 + y^3 + z^4), Map: multivariate polynomial ring -> Rq)
+(Quotient of multivariate polynomial ring by ideal (w, x^2 + y^3 + z^4), Map: R -> Rq)
 
 julia> J = ideal(R,[x,y,z,w])
 Ideal generated by
@@ -158,7 +158,7 @@ Ideal generated by
   x^2 + y^3 + z^4
 
 julia> Rq, _ = quo(R,I)
-(Quotient of multivariate polynomial ring by ideal (w, x^2 + y^3 + z^4), Map: multivariate polynomial ring -> Rq)
+(Quotient of multivariate polynomial ring by ideal (w, x^2 + y^3 + z^4), Map: R -> Rq)
 
 julia> J = ideal(R,[x,y,z,w])
 Ideal generated by
diff --git a/src/Combinatorics/SimplicialComplexes.jl b/src/Combinatorics/SimplicialComplexes.jl
index 1edd796bcb98..e00d6a293045 100644
--- a/src/Combinatorics/SimplicialComplexes.jl
+++ b/src/Combinatorics/SimplicialComplexes.jl
@@ -370,7 +370,7 @@ Return the Stanley-Reisner ring of the abstract simplicial complex `K`, as a quo
 julia>  R, _ = ZZ["a","b","c","d","e","f"];
 
 julia> stanley_reisner_ring(R, real_projective_plane())
-(Quotient of multivariate polynomial ring by ideal (a*b*c, a*b*d, a*e*f, b*e*f, a*c*f, a*d*e, c*d*e, c*d*f, b*c*e, b*d*f), Map: multivariate polynomial ring -> quotient of multivariate polynomial ring)
+(Quotient of multivariate polynomial ring by ideal (a*b*c, a*b*d, a*e*f, b*e*f, a*c*f, a*d*e, c*d*e, c*d*f, b*c*e, b*d*f), Map: R -> quotient of multivariate polynomial ring)
 ```
 """
 stanley_reisner_ring(R::MPolyRing, K::SimplicialComplex) = quo(R, stanley_reisner_ideal(R, K))
diff --git a/src/Modules/ModuleTypes.jl b/src/Modules/ModuleTypes.jl
index a2416d45c949..b771dfac76a2 100644
--- a/src/Modules/ModuleTypes.jl
+++ b/src/Modules/ModuleTypes.jl
@@ -116,7 +116,7 @@ julia> R, (x, y) = polynomial_ring(QQ, ["x", "y"])
 (Multivariate polynomial ring in 2 variables over QQ, QQMPolyRingElem[x, y])
 
 julia> F = free_module(R, 3)
-Free module of rank 3 over Multivariate polynomial ring in 2 variables over QQ
+Free module of rank 3 over R
 
 julia> f = F(sparse_row(R, [(1,x),(3,y)]))
 x*e[1] + y*e[3]
diff --git a/src/Modules/UngradedModules/FreeMod.jl b/src/Modules/UngradedModules/FreeMod.jl
index 86c3a881f3f5..e040f69abb42 100644
--- a/src/Modules/UngradedModules/FreeMod.jl
+++ b/src/Modules/UngradedModules/FreeMod.jl
@@ -37,7 +37,7 @@ The string `name` specifies how the basis vectors are printed.
 julia> R, (x, y, z) = polynomial_ring(QQ, ["x", "y", "z"]);
 
 julia> FR = free_module(R, 2)
-Free module of rank 2 over Multivariate polynomial ring in 3 variables over QQ
+Free module of rank 2 over R
 
 julia> x*FR[1]
 x*e[1]
@@ -49,7 +49,7 @@ julia> U = complement_of_prime_ideal(P);
 julia> RL, _ = localization(R, U);
 
 julia> FRL = free_module(RL, 2, "f")
-Free module of rank 2 over Localization of multivariate polynomial ring in 3 variables over QQ at complement of prime ideal (x, y, z)
+Free module of rank 2 over Localization of R at complement of prime ideal (x, y, z)
 
 julia> RL(x)*FRL[1]
 x*f[1]
diff --git a/src/Modules/UngradedModules/FreeModElem.jl b/src/Modules/UngradedModules/FreeModElem.jl
index ea29e58f9ba1..70e67c8d331c 100644
--- a/src/Modules/UngradedModules/FreeModElem.jl
+++ b/src/Modules/UngradedModules/FreeModElem.jl
@@ -84,7 +84,7 @@ julia> R, (x, y) = polynomial_ring(QQ, ["x", "y"])
 (Multivariate polynomial ring in 2 variables over QQ, QQMPolyRingElem[x, y])
 
 julia> F = FreeMod(R,3)
-Free module of rank 3 over Multivariate polynomial ring in 2 variables over QQ
+Free module of rank 3 over R
 
 julia> f = x*gen(F,1)+y*gen(F,3)
 x*e[1] + y*e[3]
diff --git a/src/Modules/UngradedModules/FreeModuleHom.jl b/src/Modules/UngradedModules/FreeModuleHom.jl
index 7053cb615649..569df691993a 100644
--- a/src/Modules/UngradedModules/FreeModuleHom.jl
+++ b/src/Modules/UngradedModules/FreeModuleHom.jl
@@ -42,10 +42,10 @@ julia> R, (x, y, z) = polynomial_ring(QQ, ["x", "y", "z"])
 (Multivariate polynomial ring in 3 variables over QQ, QQMPolyRingElem[x, y, z])
 
 julia> F = free_module(R, 3)
-Free module of rank 3 over Multivariate polynomial ring in 3 variables over QQ
+Free module of rank 3 over R
 
 julia> G = free_module(R, 2)
-Free module of rank 2 over Multivariate polynomial ring in 3 variables over QQ
+Free module of rank 2 over R
 
 julia> V = [y*G[1], x*G[1]+y*G[2], z*G[2]];
 
@@ -101,10 +101,10 @@ julia> R, (x, y, z) = polynomial_ring(QQ, ["x", "y", "z"])
 (Multivariate polynomial ring in 3 variables over QQ, QQMPolyRingElem[x, y, z])
 
 julia> F = free_module(R, 3)
-Free module of rank 3 over Multivariate polynomial ring in 3 variables over QQ
+Free module of rank 3 over R
 
 julia> G = free_module(R, 2)
-Free module of rank 2 over Multivariate polynomial ring in 3 variables over QQ
+Free module of rank 2 over R
 
 julia> V = [y*G[1], x*G[1]+y*G[2], z*G[2]]
 3-element Vector{FreeModElem{QQMPolyRingElem}}:
@@ -116,10 +116,10 @@ julia> a = hom(F, G, V)
 Map with following data
 Domain:
 =======
-Free module of rank 3 over Multivariate polynomial ring in 3 variables over QQ
+Free module of rank 3 over R
 Codomain:
 =========
-Free module of rank 2 over Multivariate polynomial ring in 3 variables over QQ
+Free module of rank 2 over R
 
 julia> a(F[2])
 x*e[1] + y*e[2]
@@ -133,10 +133,10 @@ julia> b = hom(F, G, B)
 Map with following data
 Domain:
 =======
-Free module of rank 3 over Multivariate polynomial ring in 3 variables over QQ
+Free module of rank 3 over R
 Codomain:
 =========
-Free module of rank 2 over Multivariate polynomial ring in 3 variables over QQ
+Free module of rank 2 over R
 
 julia> a == b
 true
@@ -325,10 +325,10 @@ that converts elements from $S$ into morphisms $F \to G$.
 julia> R, _ = polynomial_ring(QQ, ["x", "y", "z"]);
 
 julia> F1 = free_module(R, 3)
-Free module of rank 3 over Multivariate polynomial ring in 3 variables over QQ
+Free module of rank 3 over R
 
 julia> F2 = free_module(R, 2)
-Free module of rank 2 over Multivariate polynomial ring in 3 variables over QQ
+Free module of rank 2 over R
 
 julia> V, f = hom(F1, F2)
 (hom of (F1, F2), Map: V -> set of all homomorphisms from F1 to F2)
@@ -337,10 +337,10 @@ julia> f(V[1])
 Map with following data
 Domain:
 =======
-Free module of rank 3 over Multivariate polynomial ring in 3 variables over QQ
+Free module of rank 3 over R
 Codomain:
 =========
-Free module of rank 2 over Multivariate polynomial ring in 3 variables over QQ
+Free module of rank 2 over R
 
 ```
 
@@ -414,10 +414,10 @@ julia> R, (x, y, z) = polynomial_ring(QQ, ["x", "y", "z"])
 (Multivariate polynomial ring in 3 variables over QQ, QQMPolyRingElem[x, y, z])
 
 julia> F = free_module(R, 3)
-Free module of rank 3 over Multivariate polynomial ring in 3 variables over QQ
+Free module of rank 3 over R
 
 julia> G = free_module(R, 2)
-Free module of rank 2 over Multivariate polynomial ring in 3 variables over QQ
+Free module of rank 2 over R
 
 julia> V = [y*G[1], x*G[1]+y*G[2], z*G[2]];
 
@@ -434,7 +434,7 @@ Submodule with 1 generator
 represented as subquotient with no relations.
 Codomain:
 =========
-Free module of rank 3 over Multivariate polynomial ring in 3 variables over QQ)
+Free module of rank 3 over R)
 ```
 
 ```jldoctest
@@ -546,10 +546,10 @@ julia> R, (x, y, z) = polynomial_ring(QQ, ["x", "y", "z"])
 (Multivariate polynomial ring in 3 variables over QQ, QQMPolyRingElem[x, y, z])
 
 julia> F = free_module(R, 3)
-Free module of rank 3 over Multivariate polynomial ring in 3 variables over QQ
+Free module of rank 3 over R
 
 julia> G = free_module(R, 2)
-Free module of rank 2 over Multivariate polynomial ring in 3 variables over QQ
+Free module of rank 2 over R
 
 julia> V = [y*G[1], x*G[1]+y*G[2], z*G[2]];
 
@@ -570,7 +570,7 @@ Submodule with 3 generators
 represented as subquotient with no relations.
 Codomain:
 =========
-Free module of rank 2 over Multivariate polynomial ring in 3 variables over QQ)
+Free module of rank 2 over R)
 ```
 
 ```jldoctest
diff --git a/src/Modules/UngradedModules/FreeResolutions.jl b/src/Modules/UngradedModules/FreeResolutions.jl
index de1e53c24f87..672d8c4696e4 100644
--- a/src/Modules/UngradedModules/FreeResolutions.jl
+++ b/src/Modules/UngradedModules/FreeResolutions.jl
@@ -284,7 +284,7 @@ julia> is_complete(fr)
 false
 
 julia> fr[4]
-Free module of rank 0 over Multivariate polynomial ring in 3 variables over QQ
+Free module of rank 0 over R
 
 julia> fr
 Free resolution of M
diff --git a/src/Modules/UngradedModules/Presentation.jl b/src/Modules/UngradedModules/Presentation.jl
index c30a9d92f9f1..9bf8031f91c1 100644
--- a/src/Modules/UngradedModules/Presentation.jl
+++ b/src/Modules/UngradedModules/Presentation.jl
@@ -432,7 +432,7 @@ If `task = :only_morphism`, return only an isomorphism.
 julia> R, (x, y, z) = polynomial_ring(QQ, ["x", "y", "z"]);
 
 julia> F = free_module(R, 2)
-Free module of rank 2 over Multivariate polynomial ring in 3 variables over QQ
+Free module of rank 2 over R
 
 julia> present_as_cokernel(F)
 Submodule with 2 generators
@@ -444,7 +444,7 @@ julia> present_as_cokernel(F, :only_morphism)
 Map with following data
 Domain:
 =======
-Free module of rank 2 over Multivariate polynomial ring in 3 variables over QQ
+Free module of rank 2 over R
 Codomain:
 =========
 Submodule with 2 generators
diff --git a/src/Modules/UngradedModules/SubQuoHom.jl b/src/Modules/UngradedModules/SubQuoHom.jl
index 54b833e5e4a3..bfa2221091c9 100644
--- a/src/Modules/UngradedModules/SubQuoHom.jl
+++ b/src/Modules/UngradedModules/SubQuoHom.jl
@@ -121,7 +121,7 @@ julia> R, (x, y, z) = polynomial_ring(QQ, ["x", "y", "z"])
 (Multivariate polynomial ring in 3 variables over QQ, QQMPolyRingElem[x, y, z])
 
 julia> F = free_module(R, 1)
-Free module of rank 1 over Multivariate polynomial ring in 3 variables over QQ
+Free module of rank 1 over R
 
 julia> A = R[x; y]
 [x]
@@ -187,7 +187,7 @@ julia> R, (x, y, z) = polynomial_ring(QQ, ["x", "y", "z"])
 (Multivariate polynomial ring in 3 variables over QQ, QQMPolyRingElem[x, y, z])
 
 julia> F = free_module(R, 1)
-Free module of rank 1 over Multivariate polynomial ring in 3 variables over QQ
+Free module of rank 1 over R
 
 julia> A = R[x; y];
 
@@ -383,7 +383,7 @@ julia> R, (x, y, z) = polynomial_ring(QQ, ["x", "y", "z"])
 (Multivariate polynomial ring in 3 variables over QQ, QQMPolyRingElem[x, y, z])
 
 julia> F = free_module(R, 1)
-Free module of rank 1 over Multivariate polynomial ring in 3 variables over QQ
+Free module of rank 1 over R
 
 julia> A = R[x; y]
 [x]
@@ -602,7 +602,7 @@ Submodule with 3 generators
 represented as subquotient with no relations.
 Codomain:
 =========
-Free module of rank 2 over Multivariate polynomial ring in 3 variables over QQ
+Free module of rank 2 over R
 ```
 
 ```jldoctest
@@ -780,7 +780,7 @@ Submodule with 1 generator
 represented as subquotient with no relations.
 Codomain:
 =========
-Free module of rank 3 over Multivariate polynomial ring in 3 variables over QQ
+Free module of rank 3 over R
 ```
 
 ```jldoctest
diff --git a/src/Modules/UngradedModules/SubquoModule.jl b/src/Modules/UngradedModules/SubquoModule.jl
index 83821631c1d2..8c66a77c44a6 100644
--- a/src/Modules/UngradedModules/SubquoModule.jl
+++ b/src/Modules/UngradedModules/SubquoModule.jl
@@ -42,7 +42,7 @@ julia> R, (x,y) = polynomial_ring(QQ, ["x", "y"])
 (Multivariate polynomial ring in 2 variables over QQ, QQMPolyRingElem[x, y])
 
 julia> F = FreeMod(R,2)
-Free module of rank 2 over Multivariate polynomial ring in 2 variables over QQ
+Free module of rank 2 over R
 
 julia> O = [x*F[1]+F[2],y*F[2]]
 2-element Vector{FreeModElem{QQMPolyRingElem}}:
@@ -187,7 +187,7 @@ free module homomorphisms with codomain `F` represented by `A` and `B`.
 julia> R, (x, y, z) = polynomial_ring(QQ, ["x", "y", "z"]);
 
 julia> FR = free_module(R, 1)
-Free module of rank 1 over Multivariate polynomial ring in 3 variables over QQ
+Free module of rank 1 over R
 
 julia> AR = R[x; y]
 [x]
@@ -214,7 +214,7 @@ julia> U = complement_of_prime_ideal(P);
 julia> RL, _ = localization(R, U);
 
 julia> FRL = free_module(RL, 1)
-Free module of rank 1 over Localization of multivariate polynomial ring in 3 variables over QQ at complement of prime ideal (x, y, z)
+Free module of rank 1 over Localization of R at complement of prime ideal (x, y, z)
 
 julia> ARL = RL[x; y]
 [x]
@@ -571,7 +571,7 @@ Return the cokernel of `A` as an object of type `SubquoModule` with ambient free
 julia> R, (x,y,z) = polynomial_ring(QQ, ["x", "y", "z"]);
 
 julia> F = free_module(R, 2)
-Free module of rank 2 over Multivariate polynomial ring in 3 variables over QQ
+Free module of rank 2 over R
 
 julia> A = R[x y; 2*x^2 3*y^2]
 [    x       y]
@@ -658,7 +658,7 @@ Return the image of `A` as an object of type `SubquoModule` with ambient free mo
 julia> R, (x,y,z) = polynomial_ring(QQ, ["x", "y", "z"]);
 
 julia> F = free_module(R, 2)
-Free module of rank 2 over Multivariate polynomial ring in 3 variables over QQ
+Free module of rank 2 over R
 
 julia> A = R[x y; 2*x^2 3*y^2]
 [    x       y]
@@ -838,7 +838,7 @@ julia> R, (x, y, z) = polynomial_ring(QQ, ["x", "y", "z"])
 (Multivariate polynomial ring in 3 variables over QQ, QQMPolyRingElem[x, y, z])
 
 julia> F = free_module(R, 1)
-Free module of rank 1 over Multivariate polynomial ring in 3 variables over QQ
+Free module of rank 1 over R
 
 julia> AM = R[x;]
 [x]
@@ -966,7 +966,7 @@ julia> R, (x, y, z) = polynomial_ring(QQ, ["x", "y", "z"])
 (Multivariate polynomial ring in 3 variables over QQ, QQMPolyRingElem[x, y, z])
 
 julia> F = free_module(R, 1)
-Free module of rank 1 over Multivariate polynomial ring in 3 variables over QQ
+Free module of rank 1 over R
 
 julia> AM = R[x;]
 [x]
@@ -1165,7 +1165,7 @@ julia> R, (x, y, z) = polynomial_ring(QQ, ["x", "y", "z"])
 (Multivariate polynomial ring in 3 variables over QQ, QQMPolyRingElem[x, y, z])
 
 julia> F = free_module(R, 1)
-Free module of rank 1 over Multivariate polynomial ring in 3 variables over QQ
+Free module of rank 1 over R
 
 julia> AM = R[x;]
 [x]
@@ -1347,7 +1347,7 @@ julia> R, (x, y, z) = polynomial_ring(QQ, ["x", "y", "z"])
 (Multivariate polynomial ring in 3 variables over QQ, QQMPolyRingElem[x, y, z])
 
 julia> F = free_module(R, 1)
-Free module of rank 1 over Multivariate polynomial ring in 3 variables over QQ
+Free module of rank 1 over R
 
 julia> AM = R[x;]
 [x]
@@ -1450,7 +1450,7 @@ julia> R, (x, y, z) = polynomial_ring(QQ, ["x", "y", "z"])
 (Multivariate polynomial ring in 3 variables over QQ, QQMPolyRingElem[x, y, z])
 
 julia> F = free_module(R, 1)
-Free module of rank 1 over Multivariate polynomial ring in 3 variables over QQ
+Free module of rank 1 over R
 
 julia> AM = R[x;]
 [x]
diff --git a/src/Modules/UngradedModules/SubquoModuleElem.jl b/src/Modules/UngradedModules/SubquoModuleElem.jl
index 55e3fd35036d..5e25c8d06ab1 100644
--- a/src/Modules/UngradedModules/SubquoModuleElem.jl
+++ b/src/Modules/UngradedModules/SubquoModuleElem.jl
@@ -624,7 +624,7 @@ Submodule with 3 generators
 represented as subquotient with no relations.
 Codomain:
 =========
-Free module of rank 1 over Multivariate polynomial ring in 3 variables over QQ
+Free module of rank 1 over R
 ```
 """
 function sub(M::ModuleFP{T}, V::Vector{<:ModuleFPElem{T}}; cache_morphism::Bool=false) where T
@@ -822,7 +822,7 @@ julia> proj
 Map with following data
 Domain:
 =======
-Free module of rank 1 over Multivariate polynomial ring in 3 variables over QQ
+Free module of rank 1 over R
 Codomain:
 =========
 Subquotient of Submodule with 1 generator
@@ -984,7 +984,7 @@ julia> R, (x, y, z) = polynomial_ring(QQ, ["x", "y", "z"])
 (Multivariate polynomial ring in 3 variables over QQ, QQMPolyRingElem[x, y, z])
 
 julia> F = free_module(R, 1)
-Free module of rank 1 over Multivariate polynomial ring in 3 variables over QQ
+Free module of rank 1 over R
 
 julia> A = R[x^2+y^2;]
 [x^2 + y^2]
@@ -1040,7 +1040,7 @@ julia> R, (x, y, z) = polynomial_ring(QQ, ["x", "y", "z"])
 (Multivariate polynomial ring in 3 variables over QQ, QQMPolyRingElem[x, y, z])
 
 julia> F = free_module(R, 1)
-Free module of rank 1 over Multivariate polynomial ring in 3 variables over QQ
+Free module of rank 1 over R
 
 julia> A = R[x; y]
 [x]
diff --git a/src/Rings/MPolyMap/MPolyRing.jl b/src/Rings/MPolyMap/MPolyRing.jl
index e8135a7f8c73..fd9ac903c1d6 100644
--- a/src/Rings/MPolyMap/MPolyRing.jl
+++ b/src/Rings/MPolyMap/MPolyRing.jl
@@ -53,8 +53,8 @@ julia> R, (x, y) = polynomial_ring(K, ["x", "y"]);
 
 julia> F = hom(R, R, z -> z^2, [y, x])
 Ring homomorphism
-  from multivariate polynomial ring in 2 variables over GF(2, 2)
-  to multivariate polynomial ring in 2 variables over GF(2, 2)
+  from multivariate polynomial ring in 2 variables over K
+  to multivariate polynomial ring in 2 variables over K
 defined by
   x -> y
   y -> x
diff --git a/src/Rings/MPolyQuo.jl b/src/Rings/MPolyQuo.jl
index 04c386e3f17c..24ad06baf7ca 100644
--- a/src/Rings/MPolyQuo.jl
+++ b/src/Rings/MPolyQuo.jl
@@ -332,7 +332,7 @@ julia> R, (x, y, z) = polynomial_ring(QQ, ["x", "y", "z"])
 (Multivariate polynomial ring in 3 variables over QQ, QQMPolyRingElem[x, y, z])
 
 julia> A, _ = quo(R, ideal(R, [y-x^2, z-x^3]))
-(Quotient of multivariate polynomial ring by ideal (-x^2 + y, -x^3 + z), Map: multivariate polynomial ring -> A)
+(Quotient of multivariate polynomial ring by ideal (-x^2 + y, -x^3 + z), Map: R -> A)
 
 julia> a = ideal(A, [x-y])
 Ideal generated by
@@ -361,7 +361,7 @@ julia> R, (x, y, z) = polynomial_ring(QQ, ["x", "y", "z"])
 (Multivariate polynomial ring in 3 variables over QQ, QQMPolyRingElem[x, y, z])
 
 julia> A, _ = quo(R, ideal(R, [y-x^2, z-x^3]))
-(Quotient of multivariate polynomial ring by ideal (-x^2 + y, -x^3 + z), Map: multivariate polynomial ring -> A)
+(Quotient of multivariate polynomial ring by ideal (-x^2 + y, -x^3 + z), Map: R -> A)
 
 julia> a = ideal(A, [x-y])
 Ideal generated by
@@ -1595,8 +1595,7 @@ julia> HC = gens(L[1]);
 
 julia> EMB = L[2]
 Map defined by a julia-function with inverse
-  from quotient space over:
-  Rational field with 7 generators and no relations
+  from quotient space over QQ with 7 generators and no relations
   to quotient of multivariate polynomial ring by ideal (-x*z + y^2, -w*z + x*y, -w*y + x^2)
 
 julia> for i in 1:length(HC) println(EMB(HC[i])) end
@@ -1647,8 +1646,7 @@ julia> HC = gens(L[1]);
 
 julia> EMB = L[2]
 Map defined by a julia-function with inverse
-  from quotient space over:
-  Rational field with 7 generators and no relations
+  from quotient space over QQ with 7 generators and no relations
   to quotient of multivariate polynomial ring by ideal (x[1]*y[1] - x[2]*y[2])
 
 julia> for i in 1:length(HC) println(EMB(HC[i])) end
diff --git a/src/Rings/mpoly-localizations.jl b/src/Rings/mpoly-localizations.jl
index bdae06c95ac3..c64ce0297e66 100644
--- a/src/Rings/mpoly-localizations.jl
+++ b/src/Rings/mpoly-localizations.jl
@@ -1823,7 +1823,7 @@ Complement
   in multivariate polynomial ring in 2 variables over QQ
 
 julia> L, _ = localization(R, U)
-(Localization of multivariate polynomial ring in 2 variables over QQ at complement of prime ideal (x, y^2 + 1), Hom: multivariate polynomial ring -> localized ring)
+(Localization of multivariate polynomial ring in 2 variables over QQ at complement of prime ideal (x, y^2 + 1), Hom: R -> localized ring)
 
 julia> J = ideal(L,[y*(x^2+(y^2+1)^2)])
 Ideal generated by
diff --git a/src/Rings/orderings.jl b/src/Rings/orderings.jl
index ac309e07c25f..c038c3f83dd5 100644
--- a/src/Rings/orderings.jl
+++ b/src/Rings/orderings.jl
@@ -1571,7 +1571,7 @@ julia> cmp(lex([x,y,z]), z, one(R))
 1
 
 julia> F = free_module(R, 2)
-Free module of rank 2 over Multivariate polynomial ring in 3 variables over QQ
+Free module of rank 2 over R
 
 julia> cmp(lex(R)*invlex(F), F[1], F[2])
 -1
@@ -1931,7 +1931,7 @@ Return the ring ordering induced by `ord`.
 julia> R, (w, x, y, z) = polynomial_ring(QQ, ["w", "x", "y", "z"]);
 
 julia> F = free_module(R, 3)
-Free module of rank 3 over Multivariate polynomial ring in 4 variables over QQ
+Free module of rank 3 over R
 
 julia> o = invlex(gens(F))*degrevlex(R)
 invlex([gen(1), gen(2), gen(3)])*degrevlex([w, x, y, z])