# semigroup

Definition from Wiktionary, the free dictionary

## Contents

## English[edit]

### Etymology[edit]

From *semi-* + *group*, reflecting the fact that not all the conditions required for a group are required for a **semigroup**. (Specifically, the requirements for the existence of identity and inverse elements are omitted.)

### Noun[edit]

**semigroup** (*plural* **semigroups**)

- (mathematics) Any set for which there is a binary operation that is closed and associative.
**1961**, Alfred Hoblitzelle Clifford, G. B. Preston,*The Algebraic Theory of Semigroups*(page 70)- If a
**semigroup***S*contains a zeroid, then every left zeroid is also a right zeroid, and vice versa, and the set*K*of all the zeroids of*S*is the kernel of*S*.

- If a
**1988**, A. Ya Aǐzenshtat, Boris M. Schein (translator),*On Ideals of*, Ben Silver (editor),**Semigroups**of Endomorphisms*Nineteen Papers on Algebraic*, American Mathematical Society Translations, Series 2, Volume 139, page 11,**Semigroups**- It follows naturally that various classes of ordered sets can be characterized by semigroup properties of endomorphism
**semigroups**.

- It follows naturally that various classes of ordered sets can be characterized by semigroup properties of endomorphism
**2012**, Jorge Almeida, Benjamin Steinberg,*Syntactic and Global*, Jean-Camille Birget, Stuart Margolis, John Meakin, Mark V. Sapir (editors),**Subgroup**Theory: A Synthesis Approach*Algorithmic Problems in Groups and*, page 5,**Semigroups**- If one considers the variety of
**semigroups**, one has the binary operation of multiplication defined on every**semigroup**.

- If one considers the variety of

#### Translations[edit]

set for which a closed associative binary operation is defined

#### Derived terms[edit]

#### Hypernyms[edit]

- (set for which a closed associative binary operation is defined): magma