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Homesemigroup

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# semigroup

A semigroup $G$ is a set together with a binary operation $\cdot:G\times G\longrightarrow G$ which satisfies the associative property: $(a\cdot b)\cdot c=a\cdot(b\cdot c)$ for all $a,b,c\in G$.

The set $G$ is not required to be nonempty.

Let $G,H$ be two semigroups. A *semigroup homomorphism* from $G$ to $H$ is a function $f:G\to H$ such that $f(ab)=f(a)f(b)$.

Defines:

semigroup homomorphism

Related:

groupoid, Band2, SubmonoidSubsemigroup, NullSemigroup, ZeroElements, Monoid

Synonym:

homomorphism

Type of Math Object:

Definition

Major Section:

Reference

Groups audience:

## Mathematics Subject Classification

20M99*no label found*

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