semigroup
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.
- 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 Translations, Series 2, Volume 139, page 11,
- It follows naturally that various classes of ordered sets can be characterized by semigroup properties of endomorphism semigroups.
- 2012, Jorge Almeida, Benjamin Steinberg, “Syntactic and Global Subgroup Theory: A Synthesis Approach”, in Jean-Camille Birget, Stuart Margolis, John Meakin, Mark V. Sapir, editors, Algorithmic Problems in Groups and Semigroups, page 5:
- If one considers the variety of semigroups, one has the binary operation of multiplication defined on every semigroup.
Hypernyms edit
- (set for which a closed associative binary operation is defined): magma
Hyponyms edit
Derived terms edit
Translations edit
set for which a closed associative binary operation is defined
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