Word.ws English Dictionary

semigroup

semigroup noun: any set for which there is a binary operation that is closed and associative.

Noun

semigroup (plural semigroups)

  1. Any set for which there is a binary operation that is closed and associative.
    • 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.1961, Alfred Hoblitzelle Clifford, G. B. Preston, The Algebraic Theory of Semigroups, page 70
    • It follows naturally that various classes of ordered sets can be characterized by semigroup properties of endomorphism semigroups.1988, A. Ya Aǐzenshtat, Boris M. Schein (translator), On Ideals of Semigroups of Endomorphisms, Ben Silver (editor), Nineteen Papers on Algebraic Semigroups, American Mathematical Society...

Examples of semigroup in a sentence

  • Pseudovarieties are of particular importance in the study of finite semigroups and hence in formal language theory.
  • Abstractly, additive number theory includes the study of abelian groups and commutative semigroups with an addition operation.
  • Every finite semigroup has an idempotent element.

All 11 example sentences with semigroup

Forms of semigroup

pluralsemigroups

Origin of semigroup

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.)

Words formed from semigroup

Phrases with semigroup

Questions about semigroup

What does semigroup mean?
Semigroup means any set for which there is a binary operation that is closed and associative.
What part of speech is semigroup?
Semigroup is a noun.
What is the plural of semigroup?
The plural of semigroup is semigroups.

Words near semigroup in the dictionary

  1. semigration
  2. semigratuitous
  3. semigregarious
  4. semigroud
  5. semigrouds
  6. semigroup
  7. semigroup homomorphism
  8. semigroup homomorphisms
  9. semigroupoid
  10. semigroupoids
  11. semigroups

Source and license

Adapted from Wiktionary: semigroup (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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