On Modules over Groups

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Uc M., ONES O., ALKAN M.

FILOMAT, vol.30, no.4, pp.1021-1027, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 30 Issue: 4
  • Publication Date: 2016
  • Doi Number: 10.2298/fil1604021u
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1021-1027
  • Keywords: Gruop rings, Projective modules and Injective modules
  • Akdeniz University Affiliated: Yes

Abstract

For a finite group G, by the endomorphism ring of a module M over a commutative ring R, we define a structure for M to make it an RG-module so that we study the relations between the properties of R-modules and RG-modules. Mainly, we prove that Rad(R)M is an RG-submodule of M if M is an RG-module; also Rad(R)M subset of Rad(RG)M where Rad(A)M is the intersection of the maximal A-submodule of module M over a ring A. We also verify that M is an injective (projective) R-module if and only if M is an injective (projective) RG-module.