Vanishing of relative homology and depth of tensor products

JOURNAL OF ALGEBRA

卷:478

Article

Celikbas, Olgur¹  Liang, Li²  Sadeghi, Arash³ 

[1] West Virginia Univ, Dept Math, Morgantown, WV 26506 USA

[2] Lanzhou Jiaotong Univ, Sch Math & Phys, Lanzhou 730070, Peoples R China

[3] IPM, Inst Res Fundamental Sci, Sch Math, POB 19395-5746, Tehran, Iran

关键词: G-relative homology;    Tate homology;    Depth;    Tensor products of modules;   

DOI  :  10.1016/j.jalgebra.2017.01.043

来源: Elsevier

【 摘 要 】

For finitely generated modules M and N over a Gorenstein local ring R, one has depth M+depth N = depth (M OR N) depth R, i.e., the depth formula holds, if M and N are Tor-independent and Tate homology Tori(M, N) vanishes for all i is an element of Z. We establish the same conclusion under weaker hypotheses: if M and N are g-relative Tor-independent, then the vanishing of Tor(i)(M, N) for all i 0 is enough for the depth formula to hold. We also analyze the depth of tensor products of modules and obtain a necessary condition for the depth formula in terms of g-relative homology. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free