5 deleted 3 characters in body; edited title

# Algebra / unitialunital associative algebra: better terminology?

In Bourbaki an algebra over a commutative ring $k$ is defined to be a $k$-module $A$ together with a $k$-bilinear map $A \times A \rightarrow A$. We then have the obvious notion of morphisms of $k$-algebras. This terminology is nice, because e.g. Lie algebras are then a special kind of algebras and so on. But in 95% of my work I am using unitial unital associative $k$-algebras with unitial unital morphisms. Now, is there any better (in particular shorter) terminology available to distinguish these two cases? I don't want to add this "unital associative" and "unitial unital morphisms" all the time. Is perhaps something like prealgebra for the first case or another short word used in the literature?

4 edited tags
3 added 104 characters in body

In Bourbaki an algebra over a commutative ring $k$ is defined to be a $k$-module $A$ together with a $k$-bilinear map $A \times A \rightarrow A$. We then have the obvious notion of morphisms of $k$-algebras. This terminology is nice, because e.g. Lie algebras are then a special kind of algebras and so on. But in 95% of my work I am using unitial associative $k$-algebras with unitial morphisms. Now, is there any better (in particular shorter) terminology available to distinguish these two cases? I don't want to add this "unital associative" and "unitial morphisms" all the time. Is perhaps something like prealgebra for the first case or another short word used in the literature?

2 The questio has nothing to do with representation theory