diff --git a/experimental/LieAlgebras/src/AbstractLieAlgebra.jl b/experimental/LieAlgebras/src/AbstractLieAlgebra.jl
index 59b4aab244d1..4ba40124658b 100644
--- a/experimental/LieAlgebras/src/AbstractLieAlgebra.jl
+++ b/experimental/LieAlgebras/src/AbstractLieAlgebra.jl
@@ -246,7 +246,7 @@ function lie_algebra(
   basis::Vector{AbstractLieAlgebraElem{C}}; check::Bool=true
 ) where {C<:RingElement}
   parent_L = parent(basis[1])
-  @req all(parent(x) == parent_L for x in basis) "Elements not compatible."
+  @req all(parent(x) === parent_L for x in basis) "Elements not compatible."
   R = coefficient_ring(parent_L)
   basis_matrix = if length(basis) == 0
     matrix(R, 0, dim(L), C[])
diff --git a/experimental/LieAlgebras/src/LieAlgebra.jl b/experimental/LieAlgebras/src/LieAlgebra.jl
index 3a4db2086fa3..25f80678db9a 100644
--- a/experimental/LieAlgebras/src/LieAlgebra.jl
+++ b/experimental/LieAlgebras/src/LieAlgebra.jl
@@ -200,7 +200,7 @@ end
 Return `x`. Fails if `x` is not an element of `L`.
 """
 function (L::LieAlgebra{C})(x::LieAlgebraElem{C}) where {C<:RingElement}
-  @req L == parent(x) "Incompatible modules."
+  @req L === parent(x) "Incompatible modules."
   return x
 end
 
@@ -313,7 +313,7 @@ end
 Return the centralizer of `xs` in `L`, i.e. $\{y \in L \mid [x, y] = 0 \forall x \in xs\}$.
 """
 function centralizer(L::LieAlgebra, xs::AbstractVector{<:LieAlgebraElem})
-  @req all(x -> parent(x) == L, xs) "Incompatible Lie algebras."
+  @req all(x -> parent(x) === L, xs) "Incompatible Lie algebras."
 
   mat = zero_matrix(coefficient_ring(L), dim(L), dim(L) * length(xs))
   for (i, bi) in enumerate(basis(L))
diff --git a/experimental/LieAlgebras/src/LieAlgebraIdeal.jl b/experimental/LieAlgebras/src/LieAlgebraIdeal.jl
index da531f502482..8f0ab52dbfa2 100644
--- a/experimental/LieAlgebras/src/LieAlgebraIdeal.jl
+++ b/experimental/LieAlgebras/src/LieAlgebraIdeal.jl
@@ -203,7 +203,7 @@ Return the normalizer of `I` in `L`, i.e. $\{x \in L \mid [x, I] \subseteq I\} =
 As `I` is an ideal in `L`, this is just `L`.
 """
 function normalizer(L::LieAlgebra, I::LieAlgebraIdeal)
-  @req base_lie_algebra(I) == L "Incompatible Lie algebras."
+  @req base_lie_algebra(I) === L "Incompatible Lie algebras."
   return sub(L)
 end
 
diff --git a/experimental/LieAlgebras/src/LieAlgebraModule.jl b/experimental/LieAlgebras/src/LieAlgebraModule.jl
index 27fd6639810b..3e5e2dd9201e 100644
--- a/experimental/LieAlgebras/src/LieAlgebraModule.jl
+++ b/experimental/LieAlgebras/src/LieAlgebraModule.jl
@@ -329,10 +329,10 @@ Return `v`. Fails, in general, if `v` is not an element of `V`.
 If `V` is the dual module of the parent of `v`, return the dual of `v`.
 """
 function (V::LieAlgebraModule{C})(v::LieAlgebraModuleElem{C}) where {C<:RingElement}
-  if is_dual(V) && base_module(V) == parent(v)
+  if is_dual(V) && base_module(V) === parent(v)
     return V(coefficients(v))
   end
-  @req V == parent(v) "Incompatible modules."
+  @req V === parent(v) "Incompatible modules."
   return v
 end
 
@@ -352,7 +352,7 @@ function (V::LieAlgebraModule{C})(
 ) where {T<:LieAlgebraModuleElem{C}} where {C<:RingElement}
   if is_direct_sum(V) || is_tensor_product(V)
     @req length(a) == length(base_modules(V)) "Length of vector does not match."
-    @req all(i -> parent(a[i]) == base_modules(V)[i], 1:length(a)) "Incompatible modules."
+    @req all(i -> parent(a[i]) === base_modules(V)[i], 1:length(a)) "Incompatible modules."
     if is_direct_sum(V)
       return V(vcat([coefficients(x) for x in a]...))
     elseif is_tensor_product(V)
@@ -364,7 +364,7 @@ function (V::LieAlgebraModule{C})(
     end
   elseif is_exterior_power(V) || is_symmetric_power(V) || is_tensor_power(V)
     @req length(a) == get_attribute(V, :power) "Length of vector does not match power."
-    @req all(x -> parent(x) == base_module(V), a) "Incompatible modules."
+    @req all(x -> parent(x) === base_module(V), a) "Incompatible modules."
     mat = zero_matrix(coefficient_ring(V), 1, dim(V))
     if is_exterior_power(V)
       for (i, _inds) in enumerate(get_attribute(V, :ind_map)),
@@ -492,7 +492,7 @@ function Base.:*(x::LieAlgebraElem{C}, v::LieAlgebraModuleElem{C}) where {C<:Rin
 end
 
 function action(x::LieAlgebraElem{C}, v::LieAlgebraModuleElem{C}) where {C<:RingElement}
-  @req parent(x) == base_lie_algebra(parent(v)) "Incompatible Lie algebras."
+  @req parent(x) === base_lie_algebra(parent(v)) "Incompatible Lie algebras."
 
   cx = coefficients(x)
   V = parent(v)
@@ -733,7 +733,7 @@ function direct_sum(
   V::LieAlgebraModule{C}, Vs::LieAlgebraModule{C}...
 ) where {C<:RingElement}
   L = base_lie_algebra(V)
-  @req all(x -> base_lie_algebra(x) == L, Vs) "All modules must have the same base Lie algebra."
+  @req all(x -> base_lie_algebra(x) === L, Vs) "All modules must have the same base Lie algebra."
 
   dim_direct_sum_V = dim(V) + sum(dim, Vs; init=0)
   transformation_matrices = map(1:dim(L)) do i
@@ -769,7 +769,7 @@ function tensor_product(
   V::LieAlgebraModule{C}, Vs::LieAlgebraModule{C}...
 ) where {C<:RingElement}
   L = base_lie_algebra(V)
-  @req all(x -> base_lie_algebra(x) == L, Vs) "All modules must have the same base Lie algebra."
+  @req all(x -> base_lie_algebra(x) === L, Vs) "All modules must have the same base Lie algebra."
 
   dim_tensor_product_V = dim(V) * prod(dim, Vs; init=1)
   ind_map = collect(reverse.(ProductIterator([1:dim(Vi) for Vi in reverse([V, Vs...])])))
diff --git a/experimental/LieAlgebras/src/LieSubalgebra.jl b/experimental/LieAlgebras/src/LieSubalgebra.jl
index 3310ac565cd1..cc31839492ab 100644
--- a/experimental/LieAlgebras/src/LieSubalgebra.jl
+++ b/experimental/LieAlgebras/src/LieSubalgebra.jl
@@ -194,7 +194,7 @@ end
 Return the normalizer of `S` in `L`, i.e. $\{x \in L \mid [x, S] \subseteq S\}$.
 """
 function normalizer(L::LieAlgebra, S::LieSubalgebra)
-  @req base_lie_algebra(S) == L "Incompatible Lie algebras."
+  @req base_lie_algebra(S) === L "Incompatible Lie algebras."
 
   mat = zero_matrix(coefficient_ring(L), dim(L) + dim(S)^2, dim(L) * dim(S))
   for (i, bi) in enumerate(basis(L))
diff --git a/experimental/LieAlgebras/src/LinearLieAlgebra.jl b/experimental/LieAlgebras/src/LinearLieAlgebra.jl
index 3cc290430f0c..91820b0814ab 100644
--- a/experimental/LieAlgebras/src/LinearLieAlgebra.jl
+++ b/experimental/LieAlgebras/src/LinearLieAlgebra.jl
@@ -213,7 +213,7 @@ function lie_algebra(
   basis::Vector{LinearLieAlgebraElem{C}}; check::Bool=true
 ) where {C<:RingElement}
   parent_L = parent(basis[1])
-  @req all(parent(x) == parent_L for x in basis) "Elements not compatible."
+  @req all(parent(x) === parent_L for x in basis) "Elements not compatible."
   R = coefficient_ring(parent_L)
   n = parent_L.n
   s = map(AbstractAlgebra.obj_to_string, basis)
diff --git a/experimental/LieAlgebras/test/iso_gap_oscar-test.jl b/experimental/LieAlgebras/test/iso_gap_oscar-test.jl
index 309ba3d86645..2c0ccd46e6f6 100644
--- a/experimental/LieAlgebras/test/iso_gap_oscar-test.jl
+++ b/experimental/LieAlgebras/test/iso_gap_oscar-test.jl
@@ -2,7 +2,7 @@ import Oscar: GAPWrap
 
 function test_iso_gap_oscar(LG, oscarT; num_random_tests::Int=10)
   iso = Oscar.iso_gap_oscar(LG)
-  @test domain(iso) == LG
+  @test domain(iso) === LG
   LO = codomain(iso)
   @test LO isa oscarT
 
diff --git a/experimental/LieAlgebras/test/iso_oscar_gap-test.jl b/experimental/LieAlgebras/test/iso_oscar_gap-test.jl
index 644cca1d411c..31f9789b3648 100644
--- a/experimental/LieAlgebras/test/iso_oscar_gap-test.jl
+++ b/experimental/LieAlgebras/test/iso_oscar_gap-test.jl
@@ -2,7 +2,7 @@ import Oscar: GAPWrap
 
 function test_iso_oscar_gap(LO::LieAlgebra; num_random_tests::Int=10)
   iso = Oscar.iso_oscar_gap(LO)
-  @test domain(iso) == LO
+  @test domain(iso) === LO
   LG = codomain(iso)
   @test GAPWrap.IsLieAlgebra(LG)
   # @test codomain(Oscar.iso_gap_oscar(LG)) === LO