ON pi-MORPHIC MODULES

Harmanci A., Kose H., Kurtulmaz Y.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.42, no.4, pp.411-418, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 4
  • Publication Date: 2013
  • Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.411-418
  • Hacettepe University Affiliated: Yes

Abstract

Let R be an arbitrary ring with identity and M be a right R-module with S = End(M-R). Let f is an element of S. f is called pi-morphic if M/f(n)(M) congruent to r(M)(f(n)) for some positive integer n. A module M is called pi-morphic if every f is an element of S is pi-morphic. It is proved that M is pi-morphic and image-projective if and only if S is right pi-morphic and M generates its kernel. S is unit-it-regular if and only if M is pi-morphic and pi-Rickart if and only if M is pi-morphic and dual pi-Rickart. M is pi-morphic and image-injective if and only if S is left pi-morphic and M cogenerates its cokernel.