Unital Magma

A unital magma is a magma $(M, \cdot)$ equipped with an identity element $e \in M$ satisfying

for all $a \in M$.

This is the weakest structure requiring an identity. All monoids , loops , and groups are unital magmas.

Examples:

• Any monoid, loop, or group
• A set with a non-associative operation that still has an identity element