Artinian Modules over Group Rings
Let G be a group and suppose that G has an abelian normal subgroup A. If g H = G/A,then H acts on A by ah = a,where h =gA? H and a? A,andthis actiontransformsAintoa ZH-module(seealldetailsbelow). IfAisperiodic,then very often we may replace A by one of its primary p?components. This allows us to ass...
Guardat en:
| Autors principals: | , , |
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| Format: | Livre numérique |
| Idioma: | Anglais |
| Publicat: |
Basel :
Birkhäuser Basel
[20..].
Cham : Springer Nature |
| Edició: | 1st ed. 2007. |
| Col·lecció: | Frontiers in Mathematics
|
| Matèries: | |
| Accés en línia: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
L'impression du document génère 259 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) Numérisation de l'édition de Basel ; Boston ; Berlin : Birkhäuser, cop. 2007 |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Artinian Modules over Group Rings, Texte imprimé, 9783764391522 • Artinian modules over group rings, Leonid A. Kurdachenko, Javier Otal, Igor Ya. Subbotin, Basel, Birkhäuser, 2007, 1 vol. (VII-247 p.), Frontiers in mathematics, 3-7643-7764-X |
| Sumari: | Let G be a group and suppose that G has an abelian normal subgroup A. If g H = G/A,then H acts on A by ah = a,where h =gA? H and a? A,andthis actiontransformsAintoa ZH-module(seealldetailsbelow). IfAisperiodic,then very often we may replace A by one of its primary p?components. This allows us to assume that A is a p-subgroup, where p is a prime. This way we arrive at a p-module over the ring ZH. In this case, the structure of the lower layer P =? (A)={a? A| pa=0} 1 1 of A has a signi?cant in?uence on the structure of A. Since P is an elementary 1 abelian p-subgroup, we may think of P as a module over the ring F H,where F 1 p p is a prime ?eld of order p. The aboveapproachallows one to employ module and ring-theoreticalme- ods for the characterization of the groups considered. This relatively old idea has shownitselftobe verye?ectiveinthe theoryof?nite groups. Progressinthe study of ?nite groups naturally led to the implementation of this approach in in?nite groups that are closely related to ?nite groups, speci?cally, in in?nite groups with some?niteness conditions. It is wellknownthat inthe theory of ringsmany sign- icant results are related to ?niteness conditions, especially the classical conditions of minimality and maximality. Thus, both artinian and noetherian rings are the main subjects of the largest and the richest branches of the theories of commu- tive and non-commutative rings |
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| Descripció de l’ítem: | L'impression du document génère 259 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) Numérisation de l'édition de Basel ; Boston ; Berlin : Birkhäuser, cop. 2007 |
| Bibliografia: | Bibliogr. Index |
| ISBN: | 9783764377656 |
| ISSN: | 1660-8054 |
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