See inverse semigroup on Wiktionary
{
"forms": [
{
"form": "inverse semigroups",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "inverse semigroup (plural inverse semigroups)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
{
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [
"Entries with incorrect language header",
"Entry maintenance"
],
"source": "w"
},
{
"kind": "other",
"name": "Entries with translation boxes",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Pages with 1 entry",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Pages with entries",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with German translations",
"parents": [],
"source": "w"
},
{
"kind": "topical",
"langcode": "en",
"name": "Algebra",
"orig": "en:Algebra",
"parents": [
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
},
{
"kind": "topical",
"langcode": "en",
"name": "Group theory",
"orig": "en:Group theory",
"parents": [
"Algebra",
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
}
],
"examples": [
{
"ref": "2002, Peter G. Trotter, “A.9: Regular Semigroups”, in Aleksandr Vasilʹevich Mikhalev, Günter Pilz, editors, The Concise Handbook of Algebra, page 35:",
"text": "Examples of regular semigroups include any band, inverse semigroup or completely regular semigroup (see sections A. 2, A. 11, and A. 10); in particular, any group is a regular semigroup.",
"type": "quote"
},
{
"ref": "2008, Olexandr Ganyushkin, Volodymyr Mazorchuk, Classical Finite Transformation Semigroups: An Introduction, page v:",
"text": "Inverse semigroups form a class of semigroups which are closest (in some sense) to groups.",
"type": "quote"
},
{
"ref": "2014, Christopher Hollings, Mathematics across the Iron Curtain: A History of the Algebraic Theory of Semigroups, page 249:",
"text": "Inverse semigroups are central to modern semigroup theory: arguably, they form the most-studied class of semigroups.",
"type": "quote"
}
],
"glosses": [
"A semigroup in which every element x has an inverse y, such that x = xyx and y = yxy."
],
"id": "en-inverse_semigroup-en-noun-yBYz9z4i",
"links": [
[
"algebra",
"algebra"
],
[
"group theory",
"group theory"
],
[
"semigroup",
"semigroup"
],
[
"inverse",
"inverse"
]
],
"raw_glosses": [
"(algebra, group theory) A semigroup in which every element x has an inverse y, such that x = xyx and y = yxy."
],
"related": [
{
"word": "regular semigroup"
}
],
"topics": [
"algebra",
"group-theory",
"mathematics",
"sciences"
],
"translations": [
{
"code": "de",
"lang": "German",
"sense": "semigroup in which every element has an inverse",
"tags": [
"feminine"
],
"word": "inverse Halbgruppe"
}
]
}
],
"word": "inverse semigroup"
}
{
"forms": [
{
"form": "inverse semigroups",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "inverse semigroup (plural inverse semigroups)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"related": [
{
"word": "regular semigroup"
}
],
"senses": [
{
"categories": [
"English countable nouns",
"English entries with incorrect language header",
"English lemmas",
"English multiword terms",
"English nouns",
"English terms with quotations",
"Entries with translation boxes",
"Pages with 1 entry",
"Pages with entries",
"Terms with German translations",
"en:Algebra",
"en:Group theory"
],
"examples": [
{
"ref": "2002, Peter G. Trotter, “A.9: Regular Semigroups”, in Aleksandr Vasilʹevich Mikhalev, Günter Pilz, editors, The Concise Handbook of Algebra, page 35:",
"text": "Examples of regular semigroups include any band, inverse semigroup or completely regular semigroup (see sections A. 2, A. 11, and A. 10); in particular, any group is a regular semigroup.",
"type": "quote"
},
{
"ref": "2008, Olexandr Ganyushkin, Volodymyr Mazorchuk, Classical Finite Transformation Semigroups: An Introduction, page v:",
"text": "Inverse semigroups form a class of semigroups which are closest (in some sense) to groups.",
"type": "quote"
},
{
"ref": "2014, Christopher Hollings, Mathematics across the Iron Curtain: A History of the Algebraic Theory of Semigroups, page 249:",
"text": "Inverse semigroups are central to modern semigroup theory: arguably, they form the most-studied class of semigroups.",
"type": "quote"
}
],
"glosses": [
"A semigroup in which every element x has an inverse y, such that x = xyx and y = yxy."
],
"links": [
[
"algebra",
"algebra"
],
[
"group theory",
"group theory"
],
[
"semigroup",
"semigroup"
],
[
"inverse",
"inverse"
]
],
"raw_glosses": [
"(algebra, group theory) A semigroup in which every element x has an inverse y, such that x = xyx and y = yxy."
],
"topics": [
"algebra",
"group-theory",
"mathematics",
"sciences"
]
}
],
"translations": [
{
"code": "de",
"lang": "German",
"sense": "semigroup in which every element has an inverse",
"tags": [
"feminine"
],
"word": "inverse Halbgruppe"
}
],
"word": "inverse semigroup"
}
Download raw JSONL data for inverse semigroup meaning in All languages combined (2.1kB)
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-11-06 from the enwiktionary dump dated 2024-10-02 using wiktextract (fbeafe8 and 7f03c9b). 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.
If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.