Gorenstein injective envelopes and covers over two sided noetherian rings. Issue 5 (4th May 2017)

• Record Type: Journal Article
• Authors: Iacob, Alina
• Is Part Of: Communications in algebra. Volume 45:Issue 5(2017)
• Page Start: 2238
• Page End: 2244
• Publication Date: 2017-05-04
• Subjects: Gorenstein injective cover -- Gorenstein injective envelope -- Gorenstein injective module -- strongly cotorsion module; 18G10 -- 18G25 -- 18G35; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2016.1233193
• Languages: English
• ISSNs: 0092-7872

Abstract

ABSTRACT: We prove that the class of Gorenstein injective modules is both enveloping and covering over a two sided noetherian ring such that the character modules of Gorenstein injective modules are Gorenstein flat. In the second part of the paper we consider the connection between the Gorenstein injective modules and the strongly cotorsion modules. We prove that when the ring R is commutative noetherian of finite Krull dimension, the class of Gorenstein injective modules coincides with that of strongly cotorsion modules if and only if the ring R is in fact Gorenstein.