Is there some established name/nomenclature for structures $\mathfrak{A} = (A,\, {\oplus},\, {\odot})$, where
- $(A,\, {\oplus})$ forms a (commutative) unital magma (in particular not associative!),
- $(A,\, {\odot})$ forms a (commutative) monoid, and
- $\odot$ distributes over $\oplus$ ?
I am looking for something like "$\mathfrak{A}$ is a skew field" or similar.