Is there a term for a magma with identity (only)?

The term "unital magma" does get used, including by Bourbaki (Algebra I, p. 12):

A magma with an identity element is called a unital magma. Here, an identity element is defined to be two-sided.

Divisibility does not imply invertibility, so they are distinct. One can have divisibility without an identity element; one needs both for invertibility. Note: a left inverse and a right inverse might not be the same, but invertibility does not demand this.

Tags:

Abstract Algebra

Group Theory

Magma

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