Binary operation/Associative/Definition

Associative operation

A binary operation

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

on a set ${}M$ is called associative, if for all ${}x,y,z\in M$ the equality

${}(x\circ y)\circ z=y\circ (x\circ z)\,$

holds.