On π-morphic modules

Harmanci A., KÖSE H., Kurtulmaz Y.

Hacettepe Journal of Mathematics and Statistics, cilt.42, sa.4, ss.411-418, 2013 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 42 Sayı: 4
  • Basım Tarihi: 2013
  • Dergi Adı: Hacettepe Journal of Mathematics and Statistics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.411-418
  • Anahtar Kelimeler: Endomorphism rings, Unit π-regular rings, π-morphic modules, π-morphic rings
  • Ankara Üniversitesi Adresli: Evet

Özet

Let R be an arbitrary ring with identity and M be a right R-module with S = End(MR). Let f ϵ S. f is called π-morphic if M/fn(M) ≌ γM(fn) for some positive integer n. A module M is called π-morphic if every f ϵ S is π-morphic. It is proved that M is π-morphic and image-projective if and only if S is right π-morphic and M generates its kernel. S is unit-π-regular if and only if M is π-morphic and π-Rickart if and only if M is π-morphic and dual π-Rickart. M is π-morphic and image-injective if and only if S is left π-morphic and M cogenerates its cokernel.