Generalized coherent domains of self-weak injective dimension at most one. Issue 5 (4th May 2019)

• Record Type: Journal Article
• Authors: Xing, Shiqi; Kim, Hwankoo
• Is Part Of: Communications in algebra. Volume 47:Issue 5(2019)
• Page Start: 1908
• Page End: 1916
• Publication Date: 2019-05-04
• Subjects: Generalized coherent ring -- Gorenstein projective module -- super finitely presented module -- 1-GFC-domain; 13D05 -- 13C11 -- 13G05; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2018.1524006
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: Let R be a commutative ring with identity. An R -module E is said to be weak injective if Ext R 1 ( N, E ) = 0 for any super finitely presented R -module N . In this article, for a domain R with quotient field K ≠ R, it is characterized when K / R as an R -module is weak injective. Also, a couple of characterizations of generalized coherent domains of self-weak injective dimension one are given. As corollaries, we characterize Gorenstein Dedekind (resp., Gorenstein Prüfer) domains.