On soluble groups of module automorphisms of finite rank

Title:

On soluble groups of module automorphisms of finite rank

Creator:

Wehrfritz, Bertram A. F

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:540e2b5c-017d-47f0-80aa-07222bff2c22
uuid:540e2b5c-017d-47f0-80aa-07222bff2c22
issn:0011-4642

Subject:

matematika, mathematics, soluble group, finite rank, module automorphisms, Noetherian module over commutative ring, 13, and 51

Type:

model:article and TEXT

Format:

print, bez média, and svazek

Description:

Let $R$ be a commutative ring, $M$ an $R$-module and $G$ a group of $R$-automorphisms of $M$, usually with some sort of rank restriction on $G$. We study the transfer of hypotheses between $M/C_M(G)$ and $[M,G]$ such as Noetherian or having finite composition length. In this we extend recent work of Dixon, Kurdachenko and Otal and of Kurdachenko, Subbotin and Chupordia. For example, suppose $[M,G]$ is $R$-Noetherian. If $G$ has finite rank, then $M/C_M(G)$ also is $R$-Noetherian. Further, if $[M,G]$ is $R$-Noetherian and if only certain abelian sections of $G$ have finite rank, then $G$ has finite rank and is soluble-by-finite. If $M/C_M(G)$ is $R$-Noetherian and $G$ has finite rank, then $[M,G]$ need not be $R$-Noetherian., Bertram A. F. Wehrfritz., and Obsahuje bibliografické odkazy

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

809-818

Source:

Czechoslovak Mathematical Journal | 2017 Volume:67 | Number:3

Harvested from:

CDK

Metadata only:

false