diff --git a/src/bases.jl b/src/bases.jl
index e9d738f..2cd8fb0 100644
--- a/src/bases.jl
+++ b/src/bases.jl
@@ -14,6 +14,12 @@ Base.eltype(b::AbstractBasis) = eltype(typeof(b))
 Base.keytype(::Type{<:AbstractBasis{T,I}}) where {T,I} = I
 Base.keytype(b::AbstractBasis) = keytype(typeof(b))
 
+key_type(b) = keytype(b)
+# `keytype(::Type{SparseVector{V,K}})` is not defined so it falls
+# back to `keytype{::Type{<:AbstractArray})` which returns `Int`.
+key_type(::Type{SparseArrays.SparseVector{V,K}}) where {V,K} = K
+key_type(v::SparseArrays.SparseVector) = key_type(typeof(v))
+
 """
     ImplicitBasis{T,I}
 Implicit bases are not stored in memory and can be potentially infinite.
diff --git a/src/mstructures.jl b/src/mstructures.jl
index fdd155a..3d59e25 100644
--- a/src/mstructures.jl
+++ b/src/mstructures.jl
@@ -41,16 +41,13 @@ struct UnsafeAddMul{M<:Union{typeof(*),MultiplicativeStructure}}
     structure::M
 end
 
-function MA.operate_to!(
-    res::SparseCoefficients,
-    ms::MultiplicativeStructure,
-    v::AbstractCoefficients,
-    w::AbstractCoefficients,
-)
+function MA.operate_to!(res, ms::MultiplicativeStructure, v, w)
+    if res === v || res === w
+        throw(ArgumentError("No alias allowed"))
+    end
     MA.operate!(zero, res)
     res = MA.operate!(UnsafeAddMul(ms), res, v, w)
-    __canonicalize!(res)
-    return res
+    return __canonicalize!(res)
 end
 
 function MA.operate!(
@@ -66,36 +63,16 @@ function MA.operate!(
     return mc
 end
 
-function MA.operate!(
-    ms::UnsafeAddMul,
-    res::SparseCoefficients,
-    v::AbstractCoefficients,
-    w::AbstractCoefficients,
-)
+function MA.operate!(ms::UnsafeAddMul, res, v, w)
     for (kv, a) in pairs(v)
         for (kw, b) in pairs(w)
-            c = ms.structure(kv, kw) # ::AbstractCoefficients
+            c = ms.structure(kv, kw)
             MA.operate!(UnsafeAddMul(*), res, a * b, c)
         end
     end
     return res
 end
 
-function MA.operate_to!(
-    res::AbstractVector,
-    ms::MultiplicativeStructure,
-    X::AbstractVector,
-    Y::AbstractVector,
-)
-    if res === X || res === Y
-        throw(ArgumentError("No alias allowed"))
-    end
-    MA.operate!(zero, res)
-    MA.operate!(UnsafeAddMul(ms), res, X, Y)
-    res = __canonicalize!(res)
-    return res
-end
-
 __canonicalize!(sv::SparseVector) = dropzeros!(sv)
 __canonicalize!(v::AbstractVector) = v
 struct DiracMStructure{Op} <: MultiplicativeStructure
diff --git a/src/types.jl b/src/types.jl
index a74ae90..0a599e6 100644
--- a/src/types.jl
+++ b/src/types.jl
@@ -43,9 +43,17 @@ struct AlgebraElement{A,T,V} <: MA.AbstractMutable
     parent::A
 end
 
-function AlgebraElement(coeffs::AbstractVector, A::AbstractStarAlgebra)
+function _sanity_checks(coeffs, A::AbstractStarAlgebra)
+    @assert key_type(coeffs) == keytype(basis(A))
+end
+function _sanity_checks(coeffs::AbstractVector, A::AbstractStarAlgebra)
+    @assert key_type(coeffs) == keytype(basis(A))
     @assert Base.haslength(basis(A))
     @assert length(coeffs) == length(basis(A))
+end
+
+function AlgebraElement(coeffs, A::AbstractStarAlgebra)
+    _sanity_checks(coeffs, A)
     return AlgebraElement{typeof(A),valtype(coeffs),typeof(coeffs)}(coeffs, A)
 end