Local rings with quasi-decomposable maximal ideal

Saeed Nasseh; Ryo Takahashi

doi:10.1017/S0305004118000695

Local rings with quasi-decomposable maximal ideal

Saeed Nasseh
, Ryo Takahashi

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

26 Scopus citations

Abstract

Let (R, ) be a commutative noetherian local ring. In this paper, we prove that if is decomposable, then for any finitely generated R-module M of infinite projective dimension is a direct summand of (a direct sum of) syzygies of M. Applying this result to the case where is quasi-decomposable, we obtain several classifications of subcategories, including a complete classification of the thick subcategories of the singularity category of R.

Original language	English
Pages (from-to)	305-322
Number of pages	18
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Volume	168
Issue number	2
DOIs	https://doi.org/10.1017/S0305004118000695
State	Published - Mar 1 2020

Scopus Subject Areas

General Mathematics

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10.1017/S0305004118000695

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Local rings with quasi-decomposable maximal ideal

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