Monoids#

Definition: Monoid

A monoid \((M, v)\) is a set \(M\) equipped with an operation \(v: M \times M \to M\) which satisfies the following:

• Associativity: \(v(v(a, b), c) = v(a, v(b,c))\) for all \(a,b,c \in M\).
• Existence of a neutral element: There is some \(e \in M\) such that \(v(e,a) = v(a,e) = a\) for all \(a \in M\).