Unital magma

This article is about a standard (though not very rudimentary) definition in group theory. The article text may, however, contain more than just the basic definition
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Definition

A unital magma is a magma with an identity (i.e. neutral) element. That is, a unital magma is a set $M$ with a binary operation $*:M\to M$ such that there exists $e\in M$ with $e*m=m*e=m$ for all $m\in M$ .