On Submodules of Modules over Group Rings

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ÖNEŞ O., ALKAN M., Uc M.

FILOMAT, vol.34, no.2, pp.575-582, 2020 (SCI-Expanded)

  • Publication Type: Article / Article
  • Volume: 34 Issue: 2
  • Publication Date: 2020
  • Doi Number: 10.2298/fil2002575o
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Page Numbers: pp.575-582
  • Keywords: Group ring, Group Module, Module Filtration, Dimension Subgroup
  • Open Archive Collection: AVESIS Open Access Collection
  • Akdeniz University Affiliated: Yes

Abstract

In this paper, we find some connections between submodules of a module over a group ring RG and subgroups of a group G. Also, we prove that there is a direct connection between conjugate elements of G and RG-submodules of M. Finally, we show that there is a correspondence between the associative powers Delta(i)(M) (G) of Delta(M)(G) and ith dimension subgroups del(Delta(i)(R)(G)) of G over R.