See lie over in All languages combined, or Wiktionary
{ "forms": [ { "form": "lies over", "tags": [ "present", "singular", "third-person" ] }, { "form": "lying over", "tags": [ "participle", "present" ] }, { "form": "lay over", "tags": [ "past" ] }, { "form": "lain over", "tags": [ "participle", "past" ] } ], "head_templates": [ { "args": { "1": "lie<,,lay,lain> over" }, "expansion": "lie over (third-person singular simple present lies over, present participle lying over, simple past lay over, past participle lain over)", "name": "en-verb" } ], "lang": "English", "lang_code": "en", "pos": "verb", "senses": [ { "categories": [], "glosses": [ "To be deferred to a future occasion." ], "id": "en-lie_over-en-verb-GAabE9zZ", "raw_glosses": [ "(intransitive) To be deferred to a future occasion." ], "tags": [ "intransitive" ] }, { "categories": [ { "kind": "topical", "langcode": "en", "name": "Algebra", "orig": "en:Algebra", "parents": [ "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "_dis": "13 87", "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w+disamb" }, { "_dis": "12 88", "kind": "other", "name": "English phrasal verbs formed with \"over\"", "parents": [], "source": "w+disamb" }, { "_dis": "11 89", "kind": "other", "name": "Pages with 1 entry", "parents": [], "source": "w+disamb" }, { "_dis": "7 93", "kind": "other", "name": "Pages with entries", "parents": [], "source": "w+disamb" } ], "examples": [ { "ref": "1971, Max D. Larsen, Paul J. McCarthy, Multiplicative Theory of Ideals, Academic Press, page 84:", "text": "Let R be a subring of a ring R′ which is integral over R. If P is a prime ideal of R, then there is a prime ideal P′ of R′ that lies over P. Moreover, if P′ and P″ are prime ideals of R′ that lie over P and if P′ ⊆ P″, then P′ = P″.", "type": "quote" }, { "ref": "2012, A. Barlotti, E.W. Ellers, P. Plaumann, K. Strambach, Generators and Relations in Groups and Geometries, Springer Science & Business Media, page 369:", "text": "Let R ⊆ S be integral domains such that R is integrally closed and S is integral over R. Suppose that P′ ⊆ P are prime ideals of R. Let Q be a prime ideal of S which lies over P. Then Q contains a prime ideal Q′ of S that lies over P′.", "type": "quote" } ], "glosses": [ "To intersect with R at some other prime ideal p; q lies over p if and only if q∩R=p." ], "id": "en-lie_over-en-verb-5S4J6FuY", "links": [ [ "algebra", "algebra" ], [ "ring theory", "ring theory" ], [ "prime ideal", "prime ideal" ], [ "ring", "ring" ], [ "subring", "subring" ], [ "intersect", "intersect" ], [ "if and only if", "if and only if" ] ], "qualifier": "ring theory", "raw_glosses": [ "(transitive, algebra, ring theory, of a prime ideal q of a ring R' with subring R) To intersect with R at some other prime ideal p; q lies over p if and only if q∩R=p." ], "raw_tags": [ "of a prime ideal q of a ring R' with subring R" ], "synonyms": [ { "word": "lie above" } ], "tags": [ "transitive" ], "topics": [ "algebra", "mathematics", "sciences" ] } ], "word": "lie over" }
{ "categories": [ "English entries with incorrect language header", "English lemmas", "English multiword terms", "English phrasal verbs", "English phrasal verbs formed with \"over\"", "English verbs", "Pages with 1 entry", "Pages with entries" ], "forms": [ { "form": "lies over", "tags": [ "present", "singular", "third-person" ] }, { "form": "lying over", "tags": [ "participle", "present" ] }, { "form": "lay over", "tags": [ "past" ] }, { "form": "lain over", "tags": [ "participle", "past" ] } ], "head_templates": [ { "args": { "1": "lie<,,lay,lain> over" }, "expansion": "lie over (third-person singular simple present lies over, present participle lying over, simple past lay over, past participle lain over)", "name": "en-verb" } ], "lang": "English", "lang_code": "en", "pos": "verb", "senses": [ { "categories": [ "English intransitive verbs" ], "glosses": [ "To be deferred to a future occasion." ], "raw_glosses": [ "(intransitive) To be deferred to a future occasion." ], "tags": [ "intransitive" ] }, { "categories": [ "English terms with quotations", "English transitive verbs", "en:Algebra" ], "examples": [ { "ref": "1971, Max D. Larsen, Paul J. McCarthy, Multiplicative Theory of Ideals, Academic Press, page 84:", "text": "Let R be a subring of a ring R′ which is integral over R. If P is a prime ideal of R, then there is a prime ideal P′ of R′ that lies over P. Moreover, if P′ and P″ are prime ideals of R′ that lie over P and if P′ ⊆ P″, then P′ = P″.", "type": "quote" }, { "ref": "2012, A. Barlotti, E.W. Ellers, P. Plaumann, K. Strambach, Generators and Relations in Groups and Geometries, Springer Science & Business Media, page 369:", "text": "Let R ⊆ S be integral domains such that R is integrally closed and S is integral over R. Suppose that P′ ⊆ P are prime ideals of R. Let Q be a prime ideal of S which lies over P. Then Q contains a prime ideal Q′ of S that lies over P′.", "type": "quote" } ], "glosses": [ "To intersect with R at some other prime ideal p; q lies over p if and only if q∩R=p." ], "links": [ [ "algebra", "algebra" ], [ "ring theory", "ring theory" ], [ "prime ideal", "prime ideal" ], [ "ring", "ring" ], [ "subring", "subring" ], [ "intersect", "intersect" ], [ "if and only if", "if and only if" ] ], "qualifier": "ring theory", "raw_glosses": [ "(transitive, algebra, ring theory, of a prime ideal q of a ring R' with subring R) To intersect with R at some other prime ideal p; q lies over p if and only if q∩R=p." ], "raw_tags": [ "of a prime ideal q of a ring R' with subring R" ], "synonyms": [ { "word": "lie above" } ], "tags": [ "transitive" ], "topics": [ "algebra", "mathematics", "sciences" ] } ], "word": "lie over" }
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This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2025-01-08 from the enwiktionary dump dated 2025-01-01 using wiktextract (9a96ef4 and 4ed51a5). 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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