Definition 2.5.5.  Let M be a monoid, a, b ∈ M. We define:
a • b:= ab if M = [M, , e] (M is a set, :M × M → M is an operation on M, e ∈ M such that (M, , e) forms a monoid)
Remarks.

This definition lets us multiply elements without decomposing the monoid.