2019/03/11 by Olgur Celikbas, Liang Li, Li Liang +6
Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.AC #msc:13D05 #msc:13D07
paper · pdf · doi:10.48550/arxiv.1903.04091
Final version; to appear in Acta Math. Sin. (Engl. Ser.)
arxiv created 2022/01/21 · arxiv updated 2022/01/24
In this paper we are concerned with absolute, relative and Tate Tor modules. In the first part of the paper we generalize a result of Avramov and Martsinkovsky by using the Auslander-Buchweitz approximation theory, and obtain a new exact sequence connecting absolute Tor modules with relative and Tate Tor modules. In the second part of the paper we consider a depth equality, called the depth formula, which has been initially introduced by Auslander and developed further by Huneke and Wiegand. As an application of our main result, we generalize a result of Yassemi and give a new sufficient condition implying the depth formula to hold for modules of finite Gorenstein and finite injective dimension.