When is there a nontrivial extension-closed subcategory?

2011/01/05 by Ryo Takahashi, Takahashi, Ryo · 1 citation
Mathematics · #13C60 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1101.0991

openalex publication_date 2011/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let R be a commutative Noetherian local ring, and denote by mod R the category of finitely generated R-modules. In this paper, we consider when mod R has a nontrivial extension-closed subcategory. We prove that this is the case if there are part of a minimal system of generators x,y of the maximal ideal with xy=0, and that it holds if R is a stretched Artinian Gorenstein local ring which is not a hypersurface.

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• Extension-closed subcategories over hypersurfaces of finite or countable CM-representation type

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