diff --git a/src/algebra_elts.jl b/src/algebra_elts.jl
index e2e160b..44954df 100644
--- a/src/algebra_elts.jl
+++ b/src/algebra_elts.jl
@@ -15,13 +15,13 @@ function Base.deepcopy_internal(a::AlgebraElement, id::IdDict)
 end
 
 # call overload:
-(a::AlgebraElement)(x) = coeffs(a)[basis(parent(a))[x]]
-Base.setindex!(a::AlgebraElement, v, idx) = a.coeffs[basis(parent(a))[idx]] = v
+(a::AlgebraElement)(x) = coeffs(a)[basis(a)[x]]
+Base.setindex!(a::AlgebraElement, v, idx) = a.coeffs[basis(a)[idx]] = v
 
 # AlgebraElement specific functions
 
 function supp(a::AlgebraElement)
-    b = basis(parent(a))
+    b = basis(a)
     return [b[i] for (i, _) in nonzero_pairs(coeffs(a))]
 end
 
diff --git a/src/types.jl b/src/types.jl
index 11a37d5..b3e9b59 100644
--- a/src/types.jl
+++ b/src/types.jl
@@ -36,8 +36,9 @@ Base.parent(a::AlgebraElement) = a.parent
 Base.eltype(a::AlgebraElement) = valtype(coeffs(a))
 coeffs(a::AlgebraElement) = a.coeffs
 function coeffs(x::AlgebraElement, b::AbstractBasis)
-    return coeffs(coeffs(x), basis(parent(x)), b)
+    return coeffs(coeffs(x), basis(x), b)
 end
+basis(a::AlgebraElement) = basis(parent(a))
 
 function AlgebraElement(coeffs, A::AbstractStarAlgebra)
     _sanity_checks(coeffs, A)
@@ -87,7 +88,7 @@ function Base.isone(a::AlgebraElement)
     if basis(A) isa DiracBasis
         return c == cfs1
     else
-        dc = coeffs(c, basis(parent(a)), DiracBasis{UInt}(object(parent(a))))
+        dc = coeffs(c, basis(a), DiracBasis{UInt}(object(parent(a))))
         return dc == cfs1
     end
 end
diff --git a/test/group_algebra.jl b/test/group_algebra.jl
index 0dc2c25..6804b6b 100644
--- a/test/group_algebra.jl
+++ b/test/group_algebra.jl
@@ -115,7 +115,7 @@
         z = sum((one(RG) - RG(g)) * star(one(RG) - RG(g)) for g in G)
         @test SA.aug(z) == 0
 
-        @test SA.supp(z) == sort(collect(basis(parent(z))))
+        @test SA.supp(z) == sort(collect(basis(z)))
         @test SA.supp(RG(1) + RG(g)) == [one(G), g]
         @test SA.supp(a) == [one(G), h, g]