diff --git a/src/arithmetic.jl b/src/arithmetic.jl
index 8c1c5ea..62cf6d4 100644
--- a/src/arithmetic.jl
+++ b/src/arithmetic.jl
@@ -25,3 +25,8 @@ end
 function Base.:(-)(p::_AE, q::_AE)
     return MA.operate_to!(SA._preallocate_output(-, p, q), -, p, q)
 end
+
+Base.:(*)(p::Union{_APL,_AE}, q::Polynomial{B}) where {B} = *(p, algebra_element(q))
+function Base.:(*)(α, p::Polynomial{B}) where {B}
+    return _algebra_element(MP.term(α, p.monomial), B)
+end