Finiteness properties of generalized local cohomology modules for minimax modules

• Main Authors: Sh. Payrovi, I. Khalili-Gorji, Z. Rahimi-Molaei
• Format: Article
• Language: English
• Published: Taylor & Francis Group 2017-01-01
• Series: Cogent Mathematics
• Subjects: generalized local cohomology; minimax module
• Online Access: http://dx.doi.org/10.1080/23311835.2017.1327683

Let R be a commutative Noetherian ring, I an ideal of R, M be a finitely generated R-module and t be a non-negative integer. In this paper, we introduce the concept of I, M-minimax R-modules. We show that $ \text{ Hom}_R(R/I,\, H^t_I(M,\, N)/K) $ is I,M-minimax, for all I,M-minimax submodules K of $ H^t_I(M,\, N) $, whenever N and $ H_{I}^{0}(M) $, $ H_{I}^{1}(M), \, \cdots , \, H_{I}^{t-1}(M) $ are I, M-minimax R-modules. As consequence, it is shown that $ \text{ Ass}_R H^t_I(M,\, N)/K $ is a finite set.