Matches in SemOpenAlex for { <https://semopenalex.org/work/W1991330793> ?p ?o ?g. }
Showing items 1 to 69 of
69
with 100 items per page.
- W1991330793 endingPage "1834" @default.
- W1991330793 startingPage "1818" @default.
- W1991330793 abstract "Soient k un corps de nombres et O k son anneau d'entiers. Soient l un nombre premier et m un entier naturel. Soient C (resp. H ) un groupe cyclique d'ordre l (resp. m ). Soit Γ = C ⋊ H un groupe métacyclique d'ordre lm , avec H opérant fidèlement sur C . Soient M un O k -ordre maximal dans l'algèbre semi-simple k [ Γ ] contenant O k [ Γ ] , et Cl ( M ) le groupe des classes des M -modules localement libres. On définit l'ensemble R ( M ) des classes réalisables comme étant l'ensemble des classes c ∈ Cl ( M ) telles qu'il existe une extension N / k modérément ramifiée, à groupe de Galois isomorphe à Γ , avec la classe de M ⊗ O k [ Γ ] O N est égale à c , où O N est l'anneau des entiers de N . Dans cet article, on définit un sous-ensemble de R ( M ) et on montre, par l'intermédiaire d'une description utilisant un idéal de Stickelberger, qu'il est un sous-groupe de Cl ( M ) , sous l'hypothèse que k est linéairement disjoint du l -ième corps cyclotomique sur Q . Let k be a number field and O k its ring of integers. Let l be a prime number and m a natural number. Let C (resp. H ) be a cyclic group of order l (resp. m ). Let Γ = C ⋊ H be a metacyclic group of order lm , with H acting faithfully on C . Let M be a maximal O k -order in the semi-simple algebra k [ Γ ] containing O k [ Γ ] , and Cl ( M ) its locally free class group. We define the set R ( M ) of realizable classes to be the set of classes c ∈ Cl ( M ) such that there exists a Galois extension N / k which is tame, with Galois group isomorphic to Γ , and for which [ M ⊗ O k [ Γ ] O N ] = c , where O N is the ring of integers of N . In the present article, we define a subset of R ( M ) and prove, by means of a description using a Stickelberger ideal, that it is a subgroup of Cl ( M ) , under the hypothesis that k and the l -th cyclotomic field over Q are linearly disjoint." @default.
- W1991330793 created "2016-06-24" @default.
- W1991330793 creator A5010817595 @default.
- W1991330793 creator A5022091987 @default.
- W1991330793 date "2010-08-01" @default.
- W1991330793 modified "2023-09-27" @default.
- W1991330793 title "Classes réalisables d'extensions métacycliques de degré lm" @default.
- W1991330793 cites W118774816 @default.
- W1991330793 cites W1558606648 @default.
- W1991330793 cites W1576679503 @default.
- W1991330793 cites W1596298884 @default.
- W1991330793 cites W1976182547 @default.
- W1991330793 cites W2019982704 @default.
- W1991330793 cites W2027588060 @default.
- W1991330793 cites W2029693182 @default.
- W1991330793 cites W2030431169 @default.
- W1991330793 cites W2034683398 @default.
- W1991330793 cites W2035787234 @default.
- W1991330793 cites W2043791266 @default.
- W1991330793 cites W2063380619 @default.
- W1991330793 cites W2086054319 @default.
- W1991330793 cites W2090449853 @default.
- W1991330793 cites W2149897346 @default.
- W1991330793 cites W2324357577 @default.
- W1991330793 cites W2596098897 @default.
- W1991330793 cites W2768762264 @default.
- W1991330793 cites W31819375 @default.
- W1991330793 cites W53539625 @default.
- W1991330793 cites W628895723 @default.
- W1991330793 doi "https://doi.org/10.1016/j.jnt.2009.10.007" @default.
- W1991330793 hasPublicationYear "2010" @default.
- W1991330793 type Work @default.
- W1991330793 sameAs 1991330793 @default.
- W1991330793 citedByCount "2" @default.
- W1991330793 countsByYear W19913307932013 @default.
- W1991330793 countsByYear W19913307932015 @default.
- W1991330793 crossrefType "journal-article" @default.
- W1991330793 hasAuthorship W1991330793A5010817595 @default.
- W1991330793 hasAuthorship W1991330793A5022091987 @default.
- W1991330793 hasBestOaLocation W19913307931 @default.
- W1991330793 hasConcept C138885662 @default.
- W1991330793 hasConcept C15708023 @default.
- W1991330793 hasConcept C202444582 @default.
- W1991330793 hasConcept C33923547 @default.
- W1991330793 hasConceptScore W1991330793C138885662 @default.
- W1991330793 hasConceptScore W1991330793C15708023 @default.
- W1991330793 hasConceptScore W1991330793C202444582 @default.
- W1991330793 hasConceptScore W1991330793C33923547 @default.
- W1991330793 hasIssue "8" @default.
- W1991330793 hasLocation W19913307931 @default.
- W1991330793 hasOpenAccess W1991330793 @default.
- W1991330793 hasPrimaryLocation W19913307931 @default.
- W1991330793 hasRelatedWork W1557945163 @default.
- W1991330793 hasRelatedWork W1985218657 @default.
- W1991330793 hasRelatedWork W1989920940 @default.
- W1991330793 hasRelatedWork W2036077645 @default.
- W1991330793 hasRelatedWork W2073994398 @default.
- W1991330793 hasRelatedWork W2096753949 @default.
- W1991330793 hasRelatedWork W2963341196 @default.
- W1991330793 hasRelatedWork W3103780039 @default.
- W1991330793 hasRelatedWork W3124205579 @default.
- W1991330793 hasRelatedWork W4249580765 @default.
- W1991330793 hasVolume "130" @default.
- W1991330793 isParatext "false" @default.
- W1991330793 isRetracted "false" @default.
- W1991330793 magId "1991330793" @default.
- W1991330793 workType "article" @default.