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Relevant bibliographies by topics / Realizable Galois module classes

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Academic literature on the topic 'Realizable Galois module classes'

Author: Grafiati

Published: 4 June 2021

Last updated: 4 February 2022

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Journal articles on the topic "Realizable Galois module classes"

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Byott, Nigel P., and Bouchaïb Sodaïgui. "Realizable Galois module classes for tetrahedral extensions." Compositio Mathematica 141, no. 03 (2005): 573–82. http://dx.doi.org/10.1112/s0010437x04001137.

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Bruche, Clement, and Bouchaïb Sodaïgui. "On realizable Galois module classes and Steinitz classes of nonabelian extensions." Journal of Number Theory 128, no. 4 (2008): 954–78. http://dx.doi.org/10.1016/j.jnt.2007.02.009.

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Burns, D. "On arithmetically realizable classes." Mathematical Proceedings of the Cambridge Philosophical Society 118, no. 3 (1995): 383–92. http://dx.doi.org/10.1017/s0305004100073746.

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We fix a number field L and a finite group G, and write Cl (ℤL[G]) for the reduced Grothendieck group of the category of finitely generated projective ℤL[G]-modules. We let RG denote the ring of complex characters of G, with SG the additive subgroup which is generated by the irreducible symplectic characters. We shall say that an element c ∈ Cl (ℤL[G]) is ‘(arithmetically) realizable’ if there exists a tamely ramified Galois extension N/K of number fields with L ⊆ K and an identification Gal (N/K) →˜ G via which c is the class of some Gal (N/K)-stble ℤN-ideal. We let RL(G) denote the subgroup

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4

Byott, Nigel P., and Bouchaïb Sodaïgui. "Realizable Galois module classes over the group ring for non abelian extensions." Annales de l’institut Fourier 63, no. 1 (2013): 303–71. http://dx.doi.org/10.5802/aif.2762.

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SBEITY, FARAH, and BOUCHAÏB SODAÏGUI. "CLASSES DE STEINITZ D'EXTENSIONS NON ABÉLIENNES À GROUPE DE GALOIS D'ORDRE 16 OU EXTRASPÉCIAL D'ORDRE 32 ET PROBLÈME DE PLONGEMENT." International Journal of Number Theory 06, no. 08 (2010): 1769–83. http://dx.doi.org/10.1142/s1793042110003794.

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Soient k un corps de nombres et Cl (k) son groupe des classes. Soit Γ un groupe non abélien d'ordre 16, ou un groupe extraspécial d'ordre 32. Soit Rm(k, Γ) le sous-ensemble de Cl (k) formé par les éléments qui sont réalisables par les classes de Steinitz d'extensions galoisiennes de k, modérément ramifiées et dont le groupe de Galois est isomorphe à Γ. Lorsque Γ est le groupe modulaire d'ordre 16, on suppose que k contienne une racine primitive 4ème de l'unité. Dans cet article on montre que Rm(k, Γ) est le groupe Cl (k) tout entier si le nombre des classes de k est impair. On étudie un problè

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Byott, Nigel P., and Bouchaı¨b Sodaı¨gui. "Galois module structure for dihedral extensions of degree 8: Realizable classes over the group ring." Journal of Number Theory 112, no. 1 (2005): 1–19. http://dx.doi.org/10.1016/j.jnt.2005.01.003.

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Mináč, Ján, John Swallow та Adam Topaz. "Galois module structure of (ℓ n )th classes of fields". Bulletin of the London Mathematical Society 46, № 1 (2013): 143–54. http://dx.doi.org/10.1112/blms/bdt082.

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Mináč, Ján, and John Swallow. "Galois module structure ofpth-power classes of extensions of degreep." Israel Journal of Mathematics 138, no. 1 (2003): 29–42. http://dx.doi.org/10.1007/bf02783417.

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MINÁČ, JÁN, ANDREW SCHULTZ, and JOHN SWALLOW. "GALOIS MODULE STRUCTURE OF pTH-POWER CLASSES OF CYCLIC EXTENSIONS OF DEGREE pn." Proceedings of the London Mathematical Society 92, no. 2 (2006): 307–41. http://dx.doi.org/10.1112/s0024611505015479.

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In the mid-1960s Borevi$\setminus$v\{c\} and Faddeev initiated the study of the Galois module structure of groups of \$p\$th-power classes of cyclic extensions \$K/F\$ of \$p\$th-power degree. They determined the structure of these modules in the case when \$F\$ is a local field. In this paper we determine these Galois modules for all base fields \$F\$.

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HERMAN, ALLEN. "CLIFFORD CLASSES OF PRIMITIVE CENTRAL SIMPLE G-ALGEBRAS." Journal of Algebra and Its Applications 05, no. 02 (2006): 129–44. http://dx.doi.org/10.1142/s0219498806001661.

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The problem of determining a complete set of invariants for characterizing the Clifford class of a central simple G-algebra over a field K is studied under the assumption that the algebra is simple ring. This is successful in the case of interior central simple G-algebras over K, and also when the inertia subgroup of the G-algebra is a direct factor of G. As an application of the latter, it is shown that if G is a finite abelian group, L is a Galois extension of K with Galois group G, and E is a G-algebra isomorphic to EndKV for some KG-module V, then the skew group ring of G over L ⊗K E is a

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Dissertations / Theses on the topic "Realizable Galois module classes"

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Siviero, Andrea. "Class invariants for tame Galois algebras." Phd thesis, Université Sciences et Technologies - Bordeaux I, 2013. http://tel.archives-ouvertes.fr/tel-00847787.

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Let K be a number field with ring of integers O_K and let G be a finite group.By a result of E. Noether, the ring of integers of a tame Galois extension of K with Galois group G is a locally free O_K[G]-module of rank 1.Thus, to any tame Galois extension L/K with Galois group G we can associate a class [O_L] in the locally free class group Cl(O_K[G]). The set of all classes in Cl(O_K[G]) which can be obtained in this way is called the set of realizable classes and is denoted by R(O_K[G]).In this dissertation we study different problems related to R(O_K[G]).The first part focuses on the followi

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Khalil, Maya. "Classes de Steinitz, codes cycliques de Hamming et classes galoisiennes réalisables d'extensions non abéliennes de degré p³." Thesis, Valenciennes, 2016. http://www.theses.fr/2016VALE0012/document.

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Jackson, Lee. "Realisable classes for wild extensions." Thesis, University of Exeter, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.288315.

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All, Timothy James. "On the Galois module structure of the units and ray classes of a real abelian number field." The Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1365594642.

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Book chapters on the topic "Realizable Galois module classes"

1

"Extension classes." In Multiplicative Galois Module Structure. American Mathematical Society, 1996. http://dx.doi.org/10.1090/fim/005/03.

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