See semigroup in All languages combined, or Wiktionary
Download JSON data for semigroup meaning in English (4.6kB)
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"etymology_text": "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.)",
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"word": "inverse semigroup"
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{
"ref": "1961, Alfred Hoblitzelle Clifford, G. B. Preston, The Algebraic Theory of Semigroups, page 70",
"text": "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.",
"type": "quotation"
},
{
"text": "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,\nIt follows naturally that various classes of ordered sets can be characterized by semigroup properties of endomorphism semigroups."
},
{
"ref": "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",
"text": "If one considers the variety of semigroups, one has the binary operation of multiplication defined on every semigroup.",
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"Any set for which there is a binary operation that is closed and associative."
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"sense": "set for which a closed associative binary operation is defined",
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"sense": "set for which a closed associative binary operation is defined",
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"sense": "set for which a closed associative binary operation is defined",
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"(mathematics) Any set for which there is a binary operation that is closed and associative."
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"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "bàn qún",
"sense": "set for which a closed associative binary operation is defined",
"word": "半群"
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"sense": "set for which a closed associative binary operation is defined",
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"sense": "set for which a closed associative binary operation is defined",
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{
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"lang": "German",
"sense": "set for which a closed associative binary operation is defined",
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"sense": "set for which a closed associative binary operation is defined",
"tags": [
"feminine"
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"word": "hálfgrúpa"
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{
"code": "it",
"lang": "Italian",
"sense": "set for which a closed associative binary operation is defined",
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"word": "semigruppo"
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{
"code": "pt",
"lang": "Portuguese",
"sense": "set for which a closed associative binary operation is defined",
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"word": "semigrupo"
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"word": "semigrupp"
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"word": "semigroup"
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"type": "quotation"
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"text": "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,\nIt follows naturally that various classes of ordered sets can be characterized by semigroup properties of endomorphism semigroups."
},
{
"ref": "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",
"text": "If one considers the variety of semigroups, one has the binary operation of multiplication defined on every semigroup.",
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"Any set for which there is a binary operation that is closed and associative."
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"(mathematics) Any set for which there is a binary operation that is closed and associative."
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{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "bàn qún",
"sense": "set for which a closed associative binary operation is defined",
"word": "半群"
},
{
"code": "cs",
"lang": "Czech",
"sense": "set for which a closed associative binary operation is defined",
"tags": [
"feminine"
],
"word": "pologrupa"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "set for which a closed associative binary operation is defined",
"word": "puoliryhmä"
},
{
"code": "de",
"lang": "German",
"sense": "set for which a closed associative binary operation is defined",
"tags": [
"feminine"
],
"word": "Halbgruppe"
},
{
"code": "is",
"lang": "Icelandic",
"sense": "set for which a closed associative binary operation is defined",
"tags": [
"feminine"
],
"word": "hálfgrúpa"
},
{
"code": "it",
"lang": "Italian",
"sense": "set for which a closed associative binary operation is defined",
"tags": [
"masculine"
],
"word": "semigruppo"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "set for which a closed associative binary operation is defined",
"tags": [
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"word": "semigrupo"
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{
"code": "ro",
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"sense": "set for which a closed associative binary operation is defined",
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"code": "sv",
"lang": "Swedish",
"sense": "set for which a closed associative binary operation is defined",
"word": "semigrupp"
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],
"word": "semigroup"
}
This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-05-18 from the enwiktionary dump dated 2024-05-02 using wiktextract (1d5a7d1 and 304864d). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
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