The local-global principle for the artinianness dimensions

2023/11/08 by Shen, Jingwen, Yang, Xiaoyan
#13C15 #13J10 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2311.04416

Abstract

Let R be a commutative noetherian ring and \mathfraka an ideal of R. The goal of this paper is to establish the local-global principle for the artinianness dimension r_\mathfraka(M), where r_\mathfraka(M) is the smallest integer such that the local homology module of M is not artinian. For an artinian R-module M with the set Coass_RH_r_\mathfraka(M)^\mathfraka(M) finite, we show that r_\mathfraka(M)=inf\r_\mathfrakaR_\mathfrakp(Hom_R(R_\mathfrakp,M)) \hspace0.03cm|\hspace0.03cm\mathfrakp∈ SpecR\. And the class of all modules N such that Coass_RN is finite is studied.

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