On Modules over Groups

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Uc M., ONES O., ALKAN M.

FILOMAT, cilt.30, sa.4, ss.1021-1027, 2016 (SCI-Expanded)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 30 Sayı: 4
  • Basım Tarihi: 2016
  • Doi Numarası: 10.2298/fil1604021u
  • Dergi Adı: FILOMAT
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1021-1027
  • Anahtar Kelimeler: Gruop rings, Projective modules and Injective modules
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Akdeniz Üniversitesi Adresli: Evet

Özet

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.