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Any set for which there is a binary operation that is closed and associative.
Definition source: English Wiktionary via Wiktextract
Topics: mathematics, sciences
Examples
- 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.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
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.)
Across languages
Translations
11 source translations are retained for this English entry.
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Chinese Mandarin:
半群
(bàn qún)
— set for which a closed associative binary operation is defined
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Czech:
pologrupa
— set for which a closed associative binary operation is defined
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Finnish:
puoliryhmä
— set for which a closed associative binary operation is defined
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German:
Halbgruppe
— set for which a closed associative binary operation is defined
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Icelandic:
hálfgrúpa
— set for which a closed associative binary operation is defined
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Italian:
semigruppo
— set for which a closed associative binary operation is defined
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Polish:
półgrupa
— set for which a closed associative binary operation is defined
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Portuguese:
semigrupo
— set for which a closed associative binary operation is defined
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Romanian:
semigrup
— set for which a closed associative binary operation is defined
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Slovak:
pologrupa
— set for which a closed associative binary operation is defined
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Swedish:
semigrupp
— set for which a closed associative binary operation is defined
