A generalized Serre's condition. Issue 7 (3rd July 2019)

• Record Type: Journal Article
• Authors: Holmes, Brent
• Is Part Of: Communications in algebra. Volume 47:Issue 7(2019)
• Page Start: 2689
• Page End: 2701
• Publication Date: 2019-07-03
• Subjects: Alexander dual -- cohomological dimension -- Hochster–Huneke graph -- polarization -- Reisner's criterion -- Serre condition -- simplicial complex -- Stanley–Reisner ring; 05E40 -- 05E45 -- 13C15 -- 13D02 -- 13D03 -- 13D45; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2018.1539167
• Languages: English
• ISSNs: 0092-7872

Abstract

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.