Characterizing local rings via homological dimensions and regular sequences

2004/01/05 by Shokrollah Salarian, Salarian, Shokrollah, Sean Sather-Wagstaff +3
Mathematics · #13H05 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #math.AC #msc:13H05

paper · pdf · doi:10.48550/arxiv.math/0401031

Final version, to appear in J. Pure Appl. Algebra. 9 pages. Uses XY-pic

openalex publication_date 2004/01/05 · arxiv created 2005/08/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (R,m) be a Noetherian local ring of depth d and C a semidualizing R-complex. Let M be a finite R-module and t an integer between 0 and d. If G_C-dimension of M/IM is finite for all ideals I generated by an R-regular sequence of length at most d-t then either G_C-dimension of M is at most t or C is a dualizing complex. Analogous results for other homological dimensions are also given.

Citations

• Stable module theory

Related

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• An analogue of a theorem due to Levin and Vasconcelos
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