ON THE PURE-INJECTIVITY PROFILE OF A RING

Harmanci A., Lopez-Permouth S. R., ÜNGÖR B.

COMMUNICATIONS IN ALGEBRA, vol.43, no.11, pp.4984-5002, 2015 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 43 Issue: 11
  • Publication Date: 2015
  • Doi Number: 10.1080/00927872.2014.955993
  • Journal Name: COMMUNICATIONS IN ALGEBRA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.4984-5002
  • Hacettepe University Affiliated: Yes

Abstract

An analog of the injective profile of a ring, with relative injectivity replaced by relative pure-injectivity, is investigated. Emphasis is placed on comparing and contrasting the properties of both profiles. In particular, the analog in this context of the notion of poor modules is considered and properties of pure-injectively poor modules are determined. While we do not know of any ring that does not have pure-injectively poor modules, their existence has not been determined in general. Rings having pure-injectively poor modules of various types are characterized.