On dual Rickart modules and weak dual Rickart modules

KESKİN TÜTÜNCÜ D., ORHAN ERTAŞ N., Tribak R.

ALGEBRA & DISCRETE MATHEMATICS, vol.25, no.2, pp.200-214, 2018 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 25 Issue: 2
  • Publication Date: 2018
  • Journal Name: ALGEBRA & DISCRETE MATHEMATICS
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.200-214
  • Hacettepe University Affiliated: Yes

Abstract

Let R be a ring. A right R-module M is called d-Rickart if for every endomorphism phi of M, phi(M) is a direct summand of M and it is called wd-Rickart if for every nonzero endomorphism phi of M, phi(M) contains a nonzero direct summand of M. We begin with some basic properties of (w)d-Rickart modules. Then we study direct sums of (w)d-Rickart modules and the class of rings for which every finitely generated module is (w)d-Rickart. We conclude by some structure results.