diff --git a/src/Rings/NumberField.jl b/src/Rings/NumberField.jl
index 9fae563955d3..e646c15dbf97 100644
--- a/src/Rings/NumberField.jl
+++ b/src/Rings/NumberField.jl
@@ -327,7 +327,7 @@ end
 Base.://(a::NfNSGenElem{nf_elem, Generic.MPoly{nf_elem}}, b::nf_elem) =
     NfNSGenElem(divexact(Hecke.data(a), b), parent(a))
 
-divexact(a::NfNSGenElem{nf_elem, Generic.MPoly{nf_elem}}, b::nf_elem) = a//b
+divexact(a::NfNSGenElem{nf_elem, Generic.MPoly{nf_elem}}, b::nf_elem; check::Bool=true) = a//b
 
 +(a::nf_elem, b::NfNSGenElem{nf_elem, Generic.MPoly{nf_elem}}) = b + a
 
@@ -335,7 +335,7 @@ divexact(a::NfNSGenElem{nf_elem, Generic.MPoly{nf_elem}}, b::nf_elem) = a//b
 
 Base.://(a::nf_elem, b::NfNSGenElem{nf_elem, Generic.MPoly{nf_elem}}) = a * inv(b)
 
-divexact(a::nf_elem, b::NfNSGenElem{nf_elem, Generic.MPoly{nf_elem}}) = a//b
+divexact(a::nf_elem, b::NfNSGenElem{nf_elem, Generic.MPoly{nf_elem}}; check::Bool=true) = a//b
 
 # with QQFieldElem
 +(a::NfNSGenElem{T, S}, b::QQFieldElem) where {S, T} =
@@ -347,7 +347,7 @@ divexact(a::nf_elem, b::NfNSGenElem{nf_elem, Generic.MPoly{nf_elem}}) = a//b
 Base.://(a::NfNSGenElem{T, S}, b::QQFieldElem) where {S, T} =
     NfNSGenElem(divexact(Hecke.data(a), b), parent(a))
 
-divexact(a::NfNSGenElem{T, S}, b::QQFieldElem) where {S, T} = a//b
+divexact(a::NfNSGenElem{T, S}, b::QQFieldElem; check::Bool=true) where {S, T} = a//b
 
 +(a::QQFieldElem, b::NfNSGenElem{T, S}) where {S, T} = b + a
 
@@ -355,7 +355,7 @@ divexact(a::NfNSGenElem{T, S}, b::QQFieldElem) where {S, T} = a//b
 
 Base.://(a::QQFieldElem, b::NfNSGenElem{T, S}) where {S, T} = a * inv(b)
 
-divexact(a::QQFieldElem, b::NfNSGenElem{T, S}) where {S, T} = a//b
+divexact(a::QQFieldElem, b::NfNSGenElem{T, S}; check::Bool=true) where {S, T} = a//b
 
 # with ZZRingElem
 +(a::NfNSGenElem{T, S}, b::ZZRingElem) where {S, T} =
@@ -367,7 +367,7 @@ divexact(a::QQFieldElem, b::NfNSGenElem{T, S}) where {S, T} = a//b
 Base.://(a::NfNSGenElem{T, S}, b::ZZRingElem) where {S, T} =
     NfNSGenElem(divexact(Hecke.data(a), b), parent(a))
 
-divexact(a::NfNSGenElem{T, S}, b::ZZRingElem) where {S, T} = a//b
+divexact(a::NfNSGenElem{T, S}, b::ZZRingElem; check::Bool=true) where {S, T} = a//b
 
 +(a::ZZRingElem, b::NfNSGenElem{T, S}) where {S, T} = b + a
 
@@ -375,7 +375,7 @@ divexact(a::NfNSGenElem{T, S}, b::ZZRingElem) where {S, T} = a//b
 
 Base.://(a::ZZRingElem, b::NfNSGenElem{T, S}) where {S, T} = a * inv(b)
 
-divexact(a::ZZRingElem, b::NfNSGenElem{T, S}) where {S, T} = a//b
+divexact(a::ZZRingElem, b::NfNSGenElem{T, S}; check::Bool=true) where {S, T} = a//b
 
 # with Integer
 +(a::NfNSGenElem{T, S}, b::Base.Integer) where {S, T} =
@@ -385,9 +385,9 @@ divexact(a::ZZRingElem, b::NfNSGenElem{T, S}) where {S, T} = a//b
     NfNSGenElem(Hecke.data(a) * b, parent(a))
 
 Base.://(a::NfNSGenElem{nf_elem, Generic.MPoly{nf_elem}}, b::Base.Integer) =
-    NfNSGenElem(divexact(Hecke.data(a), b), parent(a))
+    NfNSGenElem(divexact(Hecke.data(a), b; check=true), parent(a))
 
-divexact(a::NfNSGenElem{nf_elem, Generic.MPoly{nf_elem}}, b::Base.Integer) = a//b
+divexact(a::NfNSGenElem{nf_elem, Generic.MPoly{nf_elem}}, b::Base.Integer; check::Bool=true) = a//b
 
 +(a::Base.Integer, b::NfNSGenElem{T, S}) where {S, T} = b + a
 
@@ -395,7 +395,7 @@ divexact(a::NfNSGenElem{nf_elem, Generic.MPoly{nf_elem}}, b::Base.Integer) = a//
 
 Base.://(a::Base.Integer, b::NfNSGenElem{T, S}) where {S, T} = a * inv(b)
 
-divexact(a::Base.Integer, b::NfNSGenElem{T, S}) where {S, T} = a//b
+divexact(a::Base.Integer, b::NfNSGenElem{T, S}; check::Bool=true) where {S, T} = a//b
 
 # with Rational
 +(a::NfNSGenElem{T, S}, b::Base.Rational{<:Base.Integer}) where {T, S} =
@@ -407,7 +407,7 @@ divexact(a::Base.Integer, b::NfNSGenElem{T, S}) where {S, T} = a//b
 Base.://(a::NfNSGenElem{nf_elem, Generic.MPoly{nf_elem}}, b::Base.Rational{<:Base.Integer}) =
     NfNSGenElem(divexact(Hecke.data(a), b), parent(a))
 
-divexact(a::NfNSGenElem{nf_elem, Generic.MPoly{nf_elem}}, b::Base.Rational{<:Base.Integer}) =
+divexact(a::NfNSGenElem{nf_elem, Generic.MPoly{nf_elem}}, b::Base.Rational{<:Base.Integer}; check::Bool=true) =
     a//b
 
 +(a::Base.Rational{<:Base.Integer}, b::NfNSGenElem{T, S}) where {S, T} = b + a
@@ -416,7 +416,7 @@ divexact(a::NfNSGenElem{nf_elem, Generic.MPoly{nf_elem}}, b::Base.Rational{<:Bas
 
 Base.://(a::Base.Rational{<:Base.Integer}, b::NfNSGenElem{T, S}) where {S, T} = a * inv(b)
 
-divexact(a::Base.Rational{<:Base.Integer}, b::NfNSGenElem{T, S}) where {S, T} =
+divexact(a::Base.Rational{<:Base.Integer}, b::NfNSGenElem{T, S}; check::Bool=true) where {S, T} =
     a//b
 
 ################################################################################
diff --git a/src/Rings/mpoly-graded.jl b/src/Rings/mpoly-graded.jl
index e47bc8c13c0a..1142c4da8d1f 100644
--- a/src/Rings/mpoly-graded.jl
+++ b/src/Rings/mpoly-graded.jl
@@ -601,11 +601,14 @@ zero(W::MPolyDecRing) = MPolyDecRingElem(zero(forget_decoration(W)), W)
 #
 ################################################################################
 
-for T in [:(+), :(-), :(*), :divexact]
+for T in [:(+), :(-), :(*)]
   @eval ($T)(a::MPolyDecRingElem,
              b::MPolyDecRingElem) = MPolyDecRingElem($T(forget_decoration(a), forget_decoration(b)), parent(a))
 end
 
+divexact(a::MPolyDecRingElem, b::MPolyDecRingElem; check::Bool=true) = MPolyDecRingElem(divexact(forget_decoration(a), forget_decoration(b); check=check), parent(a))
+
+
 ################################################################################
 #
 #  Unitary operations
@@ -620,11 +623,11 @@ end
 #
 ################################################################################
 
-divexact(a::MPolyDecRingElem, b::RingElem) = MPolyDecRingElem(divexact(forget_decoration(a), b), parent(a))
+divexact(a::MPolyDecRingElem, b::RingElem; check::Bool=true) = MPolyDecRingElem(divexact(forget_decoration(a), b; check=check), parent(a))
 
-divexact(a::MPolyDecRingElem, b::Integer) = MPolyDecRingElem(divexact(forget_decoration(a), b), parent(a))
+divexact(a::MPolyDecRingElem, b::Integer; check::Bool=true) = MPolyDecRingElem(divexact(forget_decoration(a), b; check=check), parent(a))
 
-divexact(a::MPolyDecRingElem, b::Rational) = MPolyDecRingElem(divexact(forget_decoration(a), b), parent(a))
+divexact(a::MPolyDecRingElem, b::Rational; check::Bool=true) = MPolyDecRingElem(divexact(forget_decoration(a), b; check=check), parent(a))
 
 for T in [:(-), :(+)]
   @eval ($T)(a::MPolyDecRingElem,
diff --git a/src/Rings/mpolyquo-localizations.jl b/src/Rings/mpolyquo-localizations.jl
index 655bcc114fc3..c862808a6afe 100644
--- a/src/Rings/mpolyquo-localizations.jl
+++ b/src/Rings/mpolyquo-localizations.jl
@@ -822,11 +822,11 @@ function Base.:(/)(a::T, b::T) where {T<:MPolyQuoLocRingElem}
   return c
 end
 
-function divexact(a::Oscar.IntegerUnion, b::MPolyQuoLocRingElem)
+function divexact(a::Oscar.IntegerUnion, b::MPolyQuoLocRingElem; check::Bool=true)
   return a/b
 end
 
-function divexact(a::T, b::T) where {T<:MPolyQuoLocRingElem}
+function divexact(a::T, b::T; check::Bool=true) where {T<:MPolyQuoLocRingElem}
   return a/b
 end
 
diff --git a/src/TropicalGeometry/semiring.jl b/src/TropicalGeometry/semiring.jl
index 29cb2ba9e648..277a0aa3e99f 100644
--- a/src/TropicalGeometry/semiring.jl
+++ b/src/TropicalGeometry/semiring.jl
@@ -348,7 +348,7 @@ function Base.:(*)(x::TropicalSemiringElem{minOrMax}, y::TropicalSemiringElem{mi
     return parent(x)(data(x) + data(y)) # otherwise, return their sum
 end
 
-function divexact(x::TropicalSemiringElem{minOrMax}, y::TropicalSemiringElem{minOrMax}) where {minOrMax<:Union{typeof(min),typeof(max)}}
+function divexact(x::TropicalSemiringElem{minOrMax}, y::TropicalSemiringElem{minOrMax}; check::Bool=true) where {minOrMax<:Union{typeof(min),typeof(max)}}
     @req !iszero(y) "dividing by (tropical) zero"
     return (iszero(x) ? x : parent(x)(data(x)-data(y)))
 end