Homology of artinian and mini-max modules, II

JOURNAL OF ALGEBRA

卷:403

Article

Kubik, Bethany¹  Learner, Micah²  Sather-Wagstaff, Sean³ 

[1] Dept Math Sci, West Point, NY 10996 USA

[2] Univ Puerto Rico, Dept Math Sci, Mayaguez, PR 00681 USA

[3] NDSU Dept 2750, Dept Math, Fargo, ND 58108 USA

关键词: Ext;    Tor;    Hom;    Tensor product;    Artinian;    Noetherian;    Mini-max;    Mathis duality;    Betti number;    Bass number;   

DOI  :  10.1016/j.jalgebra.2014.01.016

来源: Elsevier

【 摘 要 】

Let R be a commutative ring, and let L and L' be R-modules. We investigate finiteness conditions (e.g., noetherian, artinian, mini-max, Maths reflexive) of the modules Ext(R)(2)(L, L') and Tor(i)(R)(L, L') when L and L' satisfy combinations of these finiteness conditions. For instance, if R is noetherian, then given R-modules M and M' such that NI is Mathis reflexive and M' is mini-max (e.g., noetherian or artinian), we prove that Ext(R)(2)(M, M'), Ext(R)(2)(M', M), and Tor(i)(R)(M, M') are Maths reflexive over R for all i >= 0 and that Ext(R)(2)(M', M)(v) congruent to Tor(i)(R)(M, M'(v)) and Ext(R)(2)(M', M)(v) congruent to Tor(i)(R)(M', M-v). (c) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free