Definition:Finite Semigroup

Definition

A finite semigroup is a semigroup of finite order.

That is, a semigroup $\struct {S, \circ}$ is a finite semigroup if and only if its underlying set $G$ is finite.

That is, a finite semigroup is a semigroup with a finite number of elements.

Also see

• Definition:Order of Structure

Sources

• 1951: Nathan Jacobson: Lectures in Abstract Algebra: Volume $\text { I }$: Basic Concepts ... (previous) ... (next): Chapter $\text{I}$: Semi-Groups and Groups: $1$: Definition and examples of semigroups