nLab
magma

A magma is a set $S$ equipped with a binary operation, that is a function from $S\times S$ to $S$.

The term ‘magma’ is from Bourbaki and intends to suggest the fluidity of the concept; special cases include semigroups, quasigroups, groups, and so on. The term ‘groupoid’ is also used, but here that word means something else.