Endo-principally projective modules

ÜNGÖR B., Agayev N., HALICIOĞLU S., Harmanci A.

Novi Sad Journal of Mathematics, cilt.43, sa.1, ss.41-49, 2013 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 43 Sayı: 1
  • Basım Tarihi: 2013
  • Dergi Adı: Novi Sad Journal of Mathematics
  • Derginin Tarandığı İndeksler: Scopus
  • Sayfa Sayıları: ss.41-49
  • Anahtar Kelimeler: Abelian modules, Baer modules, Endo-p.p. modules, Endo-principally quasi-Baer modules, Endo-reduced modules, Endo-rigid modules, Endo-semicommutative modules, Endo-symmetric modules, Quasi-Baer modules
  • Ankara Üniversitesi Adresli: Evet

Özet

Let R be an arbitrary ring with identity and M a right R-module with S = EndR(M). In this paper, we introduce a class of modules that is a generalization of principally projective (or simply p.p.) rings and Baer modules. The module M is called endo-principally projective (or simply endo-p.p.) if for any m ∈ M, lS(m) = Se for some e2 = e ∈ S. For an endo-p.p. module M, we prove that M is endo-rigid (resp., endo-reduced, endo-symmetric, endo-semicommutative) if and only if the endomorphism ring S is rigid (resp., reduced, symmetric, semicommutative), and we also prove that the module M is endo-rigid if and only if M is endo-reduced if and only if M is endo-symmetric if and only if M is endo-semicommutative if and only if M is abelian. Among others we show that if M is abelian, then every direct summand of an endo-p.p. module is also endo-p.p.