diff --git a/src/Fraction.jl b/src/Fraction.jl
index 05e5a41f5d..8440cc2513 100644
--- a/src/Fraction.jl
+++ b/src/Fraction.jl
@@ -823,6 +823,7 @@ that it will always be returned by a call to the constructor when the same
 base ring $R$ is supplied.
 """
 function fraction_field(R::Ring; cached::Bool=true)
+   @req !is_trivial(R) "Zero rings are currently not supported as coefficient ring."
    return Generic.fraction_field(R; cached=cached)
 end
 
diff --git a/src/MPoly.jl b/src/MPoly.jl
index 0af4ced8f7..7942ac86b2 100644
--- a/src/MPoly.jl
+++ b/src/MPoly.jl
@@ -1508,5 +1508,7 @@ true
 Like [`polynomial_ring(R::Ring, s::Vector{Symbol})`](@ref) but return only the
 multivariate polynomial ring.
 """
-polynomial_ring_only(R::T, s::Vector{Symbol}; internal_ordering::Symbol=:lex, cached::Bool=true) where T<:Ring =
-   mpoly_ring_type(T)(R, s, internal_ordering, cached)
+function polynomial_ring_only(R::T, s::Vector{Symbol}; internal_ordering::Symbol=:lex, cached::Bool=true) where T<:Ring
+   @req !is_trivial(R) "Zero rings are currently not supported as coefficient ring."
+   return mpoly_ring_type(T)(R, s, internal_ordering, cached)
+end
diff --git a/src/NCPoly.jl b/src/NCPoly.jl
index 0559efaafb..ded12acb62 100644
--- a/src/NCPoly.jl
+++ b/src/NCPoly.jl
@@ -764,8 +764,10 @@ end
 Like [`polynomial_ring(R::NCRing, s::Symbol)`](@ref) but return only the
 polynomial ring.
 """
-polynomial_ring_only(R::T, s::Symbol; cached::Bool=true) where T<:NCRing =
-   dense_poly_ring_type(T)(R, s, cached)
+function polynomial_ring_only(R::T, s::Symbol; cached::Bool=true) where T<:NCRing
+   @req !is_trivial(R) "Zero rings are currently not supported as coefficient ring."
+   return dense_poly_ring_type(T)(R, s, cached)
+end
 
 # Simplified constructor
 
diff --git a/src/Residue.jl b/src/Residue.jl
index 89126cb566..8247fba0c0 100644
--- a/src/Residue.jl
+++ b/src/Residue.jl
@@ -450,6 +450,7 @@ to the constructor with the same base ring $R$ and element $a$. A modulus
 of zero is not supported and throws an exception.
 """
 function residue_ring(R::Ring, a::RingElement; cached::Bool = true)
+   @req !is_trivial(R) "Zero rings are currently not supported as base ring."
    # Modulus of zero cannot be supported. E.g. A C library could not be expected to
    # do matrices over Z/0 using a Z/nZ type. The former is multiprecision, the latter not.
    iszero(a) && throw(DomainError(a, "Modulus must be nonzero"))
@@ -459,6 +460,7 @@ function residue_ring(R::Ring, a::RingElement; cached::Bool = true)
 end
 
 function residue_ring(R::PolyRing, a::RingElement; cached::Bool = true)
+   @req !is_trivial(R) "Zero rings are currently not supported as base ring."
    iszero(a) && throw(DomainError(a, "Modulus must be nonzero"))
    !is_unit(leading_coefficient(a)) && throw(DomainError(a, "Non-invertible leading coefficient"))
    T = elem_type(R)
diff --git a/src/ResidueField.jl b/src/ResidueField.jl
index 0bea998023..aa473655f2 100644
--- a/src/ResidueField.jl
+++ b/src/ResidueField.jl
@@ -490,6 +490,7 @@ residue ring parent object is cached and returned for any subsequent calls
 to the constructor with the same base ring $R$ and element $a$.
 """
 function residue_field(R::Ring, a::RingElement; cached::Bool = true)
+   @req !is_trivial(R) "Zero rings are currently not supported as base ring."
    iszero(a) && throw(DivideError())
    T = elem_type(R)
    S = EuclideanRingResidueField{T}(R(a), cached)
diff --git a/src/generic/Misc/Localization.jl b/src/generic/Misc/Localization.jl
index 490f768b67..92e75e17e9 100644
--- a/src/generic/Misc/Localization.jl
+++ b/src/generic/Misc/Localization.jl
@@ -113,6 +113,8 @@ base_ring(L::LocalizedEuclideanRing) = L.base_ring::base_ring_type(L)
 
 parent(a::LocalizedEuclideanRingElem) = a.parent
 
+characteristic(::LocalizedEuclideanRing) = characteristic(base_ring(L))
+
 ###############################################################################
 #
 #   Basic manipulation