"hypersemigroup" meaning in All languages combined

See hypersemigroup on Wiktionary

Noun [English]

Forms: hypersemigroups [plural]
Etymology: From hyper- + semigroup. Etymology templates: {{prefix|en|hyper|semigroup}} hyper- + semigroup Head templates: {{en-noun}} hypersemigroup (plural hypersemigroups)
  1. (mathematics) A nonempty set for which the set of all subsets forms a semiring. Categories (topical): Mathematics

Inflected forms

{
  "etymology_templates": [
    {
      "args": {
        "1": "en",
        "2": "hyper",
        "3": "semigroup"
      },
      "expansion": "hyper- + semigroup",
      "name": "prefix"
    }
  ],
  "etymology_text": "From hyper- + semigroup.",
  "forms": [
    {
      "form": "hypersemigroups",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "hypersemigroup (plural hypersemigroups)",
      "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": "English terms prefixed with hyper-",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with entries",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "ref": "2016, Niovi Kehayopulu, “A characterization of regular, intra-regular, left quasi-regular and semisimple hypersemigroups in terms of fuzzy sets”, in arXiv:",
          "text": "An hypersemigroup H is left (resp. right) quasi-regular if and only if, for any fuzzy subset f of S we have f#92;preceq 1#92;circf#92;circ 1#92;circf (resp. f#92;preceqf#92;circ 1#92;circf#92;circ 1) and it is semisimple if and only if, for any fuzzy subset f of S we have f#92;preceq 1#92;circf#92;circ 1#92;circf#92;circ 1.",
          "type": "quote"
        }
      ],
      "glosses": [
        "A nonempty set for which the set of all subsets forms a semiring."
      ],
      "id": "en-hypersemigroup-en-noun--n-LhPFO",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "nonempty",
          "nonempty"
        ],
        [
          "set",
          "set"
        ],
        [
          "subset",
          "subset"
        ],
        [
          "semiring",
          "semiring"
        ]
      ],
      "raw_glosses": [
        "(mathematics) A nonempty set for which the set of all subsets forms a semiring."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "hypersemigroup"
}
{
  "etymology_templates": [
    {
      "args": {
        "1": "en",
        "2": "hyper",
        "3": "semigroup"
      },
      "expansion": "hyper- + semigroup",
      "name": "prefix"
    }
  ],
  "etymology_text": "From hyper- + semigroup.",
  "forms": [
    {
      "form": "hypersemigroups",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "hypersemigroup (plural hypersemigroups)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English nouns",
        "English terms prefixed with hyper-",
        "English terms with quotations",
        "Pages with 1 entry",
        "Pages with entries",
        "en:Mathematics"
      ],
      "examples": [
        {
          "ref": "2016, Niovi Kehayopulu, “A characterization of regular, intra-regular, left quasi-regular and semisimple hypersemigroups in terms of fuzzy sets”, in arXiv:",
          "text": "An hypersemigroup H is left (resp. right) quasi-regular if and only if, for any fuzzy subset f of S we have f#92;preceq 1#92;circf#92;circ 1#92;circf (resp. f#92;preceqf#92;circ 1#92;circf#92;circ 1) and it is semisimple if and only if, for any fuzzy subset f of S we have f#92;preceq 1#92;circf#92;circ 1#92;circf#92;circ 1.",
          "type": "quote"
        }
      ],
      "glosses": [
        "A nonempty set for which the set of all subsets forms a semiring."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "nonempty",
          "nonempty"
        ],
        [
          "set",
          "set"
        ],
        [
          "subset",
          "subset"
        ],
        [
          "semiring",
          "semiring"
        ]
      ],
      "raw_glosses": [
        "(mathematics) A nonempty set for which the set of all subsets forms a semiring."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "hypersemigroup"
}

Download raw JSONL data for hypersemigroup meaning in All languages combined (1.6kB)


This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2025-01-06 from the enwiktionary dump dated 2025-01-01 using wiktextract (f889f65 and 8fbd9e8). 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.