Extension functors of cominimax modules. Issue 2 (1st February 2017)

• Record Type: Journal Article
• Authors: Hassanzadeh-Lelekaami, D.; Roshan-Shekalgourabi, H.
• Is Part Of: Communications in algebra. Volume 45:Issue 2(2017)
• Page Start: 621
• Page End: 629
• Publication Date: 2017-02-01
• Subjects: Arithmetic rank -- cominimax modules -- Krull dimension -- local cohomology modules -- minimax modules -- weakly cofinite modules; 13D45 -- 13E10 -- 13C05; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2016.1172613
• Languages: English
• ISSNs: 0092-7872

Abstract

ABSTRACT: Let R be a commutative Noetherian ring with identity and I be an ideal of R . Also, let M and N be two nonzero R -modules. We prove that the R -module E x t R i ( N, M ) is I -cominimax for all i ≥0, whenever M is I -cominimax and N is finitely generated with dim N ≤ 2. Also, it is shown that the R -module E x t R i ( N, M ) is I -cominimax for all i ≥ 0, whenever N is finitely generated and M is I -cominimax with dim M ≤ 1. As an immediate consequence, we obtain that if M is a nonzero minimax R -module such that dim H I i ( M ) ≤ 1, then for each finitely generated R -module N, E x t R j ( N, H I i ( M ) ) is I -cominimax for all i ≥ 0 and j ≥ 0. Moreover, we prove that if R is local, M is I -cominimax and N is finitely generated, then the R -module E x t R i ( N, M ) is I -weakly cofinite for all i ≥ 0, when one of the following statements holds: (i) dim N = 3 or (ii) dim M ≤ 2.