Nantilus
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...
| Auteurs principaux : | , , |
|---|---|
| Format : | Livre |
| Langue : | anglais |
| Titre complet : | Artinian Modules over Group Rings / Leonid A. Kurdachenko, Javier Otal, Igor Ya. Subbotin. |
| Édition : | 1st ed. 2007. |
| Publié : |
Basel :
Birkhäuser Basel
, [20..] Cham : Springer Nature |
| Collection : | Frontiers in mathematics (Online) |
| Accès en ligne : |
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| Reproduction de : | Numérisation de l'édition de Basel ; Boston ; Berlin : Birkhäuser, cop. 2007 |
| Contenu : | Modules with chain conditions. Ranks of groups. Some generalized nilpotent groups. Artinian modules and the socle. Reduction to subgroups of finite index. Modules over Dedekind domains. The Kovacs-Newman theorem. Hartley s classes of modules. The injectivity of some simple modules. Direct decompositions in artinian modules. On the countability of artinian modules over FC-hypercentral groups. Artinian modules over periodic abelian groups. Nearly injective modules. Artinian modules over abelian groups of finite section rank. The injective envelopes of simple modules over group rings. Quasifinite modules. Some applications: splitting over the locally nilpotent residual |
| Sujets : | |
| Documents associés : | Autre format:
Artinian Modules over Group Rings Autre format: Artinian modules over group rings |
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| 200 | 1 | |a Artinian Modules over Group Rings |f Leonid A. Kurdachenko, Javier Otal, Igor Ya. Subbotin. | |
| 205 | |a 1st ed. 2007. | ||
| 214 | 0 | |a Basel |c Birkhäuser Basel | |
| 214 | 2 | |a Cham |c Springer Nature |d [20..] | |
| 225 | 0 | |a Frontiers in Mathematics |x 1660-8054 | |
| 303 | |a L'impression du document génère 259 p. | ||
| 320 | |a Bibliogr. Index | ||
| 324 | |a Numérisation de l'édition de Basel ; Boston ; Berlin : Birkhäuser, cop. 2007 | ||
| 327 | 1 | |a Modules with chain conditions |a Ranks of groups |a Some generalized nilpotent groups |a Artinian modules and the socle |a Reduction to subgroups of finite index |a Modules over Dedekind domains |a The Kovacs-Newman theorem |a Hartley s classes of modules |a The injectivity of some simple modules |a Direct decompositions in artinian modules |a On the countability of artinian modules over FC-hypercentral groups |a Artinian modules over periodic abelian groups |a Nearly injective modules |a Artinian modules over abelian groups of finite section rank |a The injective envelopes of simple modules over group rings |a Quasifinite modules |a Some applications: splitting over the locally nilpotent residual | |
| 330 | |a 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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| 452 | | | |0 112394132 |t Artinian modules over group rings |f Leonid A. Kurdachenko, Javier Otal, Igor Ya. Subbotin |c Basel |n Birkhäuser |d 2007 |p 1 vol. (VII-247 p.) |s Frontiers in mathematics |y 3-7643-7764-X | |
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