Maximal depth property of finitely generated modules

2018/02/21 by Rahimi, Ahad
#13C14 #13C15 #13D45 #13E05 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1802.07596

Abstract

Let (R,\mathfrakm) be a Noetherian local ring and M a finitely generated R-module. We say M has maximal depth if there is an associated prime \mathfrakp of M such that depth M=dim R/\mathfrakp. In this paper, we study finitely generated modules with maximal depth. It is shown that the maximal depth property is preserved under some important module operations. Generalized Cohen--Macaulay modules with maximal depth are classified. Finally, the attached primes of Hⁱ_\mathfrakm(M) are considered for i

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