Cominimaxness with respect to ideals of dimension one

2018/01/23 by Hajar Roshan-Shekalgourabi, Roshan-Shekalgourabi, Hajar
Computer Science · Mathematics · #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1801.07760

openalex publication_date 2018/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let R be a commutative Noetherian ring, \fa be an ideal of R and M be an R-module. It is shown that if \Extⁱ_R(R/\fa,M) is minimax for all i≤ dim M, then the R-module \Extⁱ_R(N,M) is minimax for all i≥ 0 and for any finitely generated R-module N with \Supp_R(N) ⊆ V (\fa) and dim N ≤ 1. As a consequence of this result we obtain that for any \fa-torsion R-module M that \Extⁱ_R(R/\fa, M) is minimax for all i≤ dim M, all Bass numbers and all Betti numbers of M are finite. This generalizes \cite[Corollary 2.7]BNS2015. Also, some equivalent conditions for the cominimaxness of local cohomology modules with respect to ideals of dimension at most one are given.

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