Rings admitting nonzero homomorphisms between non-injective modules

ER N. F., TÜRKOĞLU Z.

COMMUNICATIONS IN ALGEBRA, vol.46, no.9, pp.4052-4063, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 46 Issue: 9
  • Publication Date: 2018
  • Doi Number: 10.1080/00927872.2018.1435789
  • Journal Name: COMMUNICATIONS IN ALGEBRA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.4052-4063
  • Keywords: Injective module, neat homomorphism, ring
  • Dokuz Eylül University Affiliated: Yes

Abstract

A variety of rings including those that are Morita equivalent to local perfect rings, two by two upper triangular matrix rings over a division ring or certain rings arising in the framework of rings described by various test modules for injectivity satisfy a common property: there is a nonzero homomorphism between any two non-injective modules. In this paper, after settling a special case inspired by a concept due to Enochs as the first step, we provide a complete characterization of the rings of the title.