A Hereditary Torsion Theory for Modules Over Integral Domains and Its Applications. Issue 4 (2nd April 2016)

• Record Type: Journal Article
• Authors: Qiao, Lei; Wang, Fanggui
• Is Part Of: Communications in algebra. Volume 44:Issue 4(2016)
• Page Start: 1574
• Page End: 1587
• Publication Date: 2016-04-02
• Subjects: Coherent domain -- g-Torsion theory -- g-Injective module -- Weak Gorenstein global dimension; 13D30 -- 13D05 -- 13D07 -- 13G05 -- 13A15; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2015.1027367
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract : In this article, we study the hereditary torsion theory defined by the set of associated primes of principle ideals of an integral domain, which is called the g -torsion theory. We first discuss some general properties of g -torsion theories, and after that give some applications of them. For example, we generalize a characterization of reflexive modules over quasi-normal domains to a class of non-Noetherian domains. Among other things, a characterization of coherent domains of weak Gorenstein global dimension at most two is also given in terms of Gorenstein projectivity (or Gorenstein flatness) of injective modules relative to the g -torsion theory.