Gorenstein Projective Resolvents. Issue 9 (1st September 2016)

• Record Type: Journal Article
• Authors: Enochs, Edgar; Estrada, Sergio; Iacob, Alina; Odabaşı, Sinem
• Is Part Of: Communications in algebra. Volume 44:Issue 9(2016)
• Page Start: 3989
• Page End: 4000
• Publication Date: 2016-09-01
• Subjects: Gorenstein projective modules -- Gorenstein ring -- Left derived functor -- Preenvelope -- Precover -- Tate homology; Primary: 13H10 -- Secondary: 18G25 -- 18G15; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2015.1065847
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract : Let R be a local commutative n -Gorenstein ring. The existence of the Gorenstein projective preenvelopes for finite R -modules is known (it was proved using duality arguments). In the present article, we compute an explicit Gorenstein projective preenvelope and a right Gorenstein projective resolution of a finite R -module. In light of this knowledge, we consider left derived functors, and Gext i (−, −). We prove a balance result for the Tate derived functor . Finally, we get an exact sequence connecting these derived functors.