2013/09/02 by Kamal Bahmanpour, Bahmanpour, Kamal, Reza Naghipour +3
Mathematics · #13D45 #13E05 #14B15 #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:13D45 #msc:13E05 #msc:14B15
paper · pdf · doi:10.48550/arxiv.1309.0431
16 pages, to appear in Houston Journal of Mathematics
arxiv created 2013/09/02 · arxiv updated 2013/09/03
In this paper, we continue the study of cominimaxness modules with respect to an ideal of a commutative Noetherian ring (cf. \citeANV), and Bass numbers of local cohomology modules. Let R denote a commutative Noetherian local ring and I an ideal of R. We first show that the Bass numbers μ0(\frak p, H2I(R)) and μ1(\frak p, H2I(R)) are finite for all \frak p∈ \Spec R, whenever R is regular. As a consequence, it follows that the Goldie dimension of H2I(R) is finite. Also, for a finitely generated R-module M of dimension d, it is shown that the Bass numbers of Hd-1I(M) are finite if and only if \ExtiR(R/I, Hd-1I(M)) be minimax for all i≥0. Finally, we prove that if dim R/I=2, then the Bass numbers of HnI(M) are finite if and only if \ExtiR(R/I, HnI(M)) be minimax, for all i≥0, where n is a non-negative integer.