Question

what is monoid in discrete mathematics?

Answer 1

A monoid is a set that is closed under an associative binary operation and has an identity element such that for all , . Note that unlike a group, its elements need not have inverses. It can also be thought of as a semigroup with an identity element. A monoid must contain at least one element.

Answer 2

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• Monoid. A monoid is a semigroup with an identity element. The identity element (denoted by e or E) of a set S is an element such that (aοe)=a, for every element a∈S.

An identity element is also called a unit element. So, a monoid holds three properties simultaneously − Closure, Associative, Identity element.