On Modules Over Group Rings

Kosan M. T., Lee T., Zhou Y.

ALGEBRAS AND REPRESENTATION THEORY, cilt.17, sa.1, ss.87-102, 2014 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 17 Sayı: 1
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1007/s10468-012-9388-5
  • Dergi Adı: ALGEBRAS AND REPRESENTATION THEORY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.87-102
  • Anahtar Kelimeler: Group ring, Group module, Maschke's Theorem, Semisimple module, Regular module, Injective module, FP-injective module
  • Gazi Üniversitesi Adresli: Hayır

Özet

Let M be a right module over a ring R and let G be a group. The set MG of all formal finite sums of the form aaEuro parts per thousand (g aaEuro parts per thousand G) m (g) g where m (g) aaEuro parts per thousand M becomes a right module over the group ring RG under addition and scalar multiplication similar to the addition and multiplication of a group ring. In this paper, we study basic properties of the RG-module MG, and characterize module properties of (MG) (RG) in terms of properties of M (R) and G. Particularly, we prove the module-theoretic versions of several well-known results on group rings, including Maschke's Theorem and the classical characterizations of right self-injective group rings and of von Neumann regular group rings.