A Generalized Serre's Condition

2017/10/07 by Holmes, Brent · 1 citation
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1710.02631

Abstract

Throughout, let R be a commutative Noetherian ring. A ring R satisfies Serre's condition (S_ℓ) if for all P ∈ \Spec R, \depth R_P ≥ min \ ℓ , dim R_P \. Serre's condition has been a topic of expanding interest. In this paper, we examine a generalization of Serre's condition (S_ℓ^j). We say a ring satisfies (S_ℓ^j) when \depth R_P ≥ min \ ℓ , dim R_P -j \ for all P ∈ \Spec R. We prove generalizations of results for rings satisfying Serre's condition.

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