Finiteness properties of local cohomology modules for $\mathfrak a$-minimax modules

Jafar Azami, Reza Naghipour, Bahram Vakili
2008 Proceedings of the American Mathematical Society  
Let R be a commutative Noetherian ring and a an ideal of R. In this paper we introduce the concept of a-minimax R-modules, and it is shown that if M is an a-minimax R-module and t a non-negative integer such that H i a (M ) is a-minimax for all i < t, then for any a-minimax submodule N of H t a (M ), the R-module Hom R (R/a, H t a (M )/N ) is a-minimax. As a consequence, it follows that the Goldie dimension of H t a (M )/N is finite, and so the associated primes of H t a (M )/N are finite. This
more » ... generalizes the main result of Brodmann and Lashgari (2000) .
doi:10.1090/s0002-9939-08-09530-0 fatcat:h3mvevyqovegzfrxfxcvzzbqdu