Binary operation/Neutral element/Definition

Neutral element

Let a set ${}M$ and a binary operation

$\circ \colon M\times M\longrightarrow M,(x,y)\longmapsto x\circ y,$

be given. An element ${}e\in M$ is called neutral element of the operation if, for all ${}x\in M$, the equalities ${}x\circ e=x=e\circ x$ hold.