Linkage of finite Gorenstein dimension modules

2011/09/29 by Mohammad T. Dibaei, Dibaei, Mohammad T., Arash Sadeghi +1
Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #math.AC

paper · pdf · doi:10.48550/arxiv.1109.6528

21 pages, Theorem 2.7 is corrected

openalex publication_date 2011/09/29 · arxiv created 2012/02/22 · arxiv updated 2012/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a horizontally linked module, over a commutative semiperfect Noetherian ring R, the connections of its invariants reduced grade, Gorenstein dimension and depth are studied. It is shown that under certain conditions the depth of a horizontally linked module is equal to the reduced grade of its linked module. The connection of the Serre condition (S_n) on an R--module of finite Gorenstein dimension with the vanishing of the local cohomology groups of its linked module is discussed.

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