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Local rings with quasi-decomposable maximal ideal

Published online by Cambridge University Press:  26 September 2018

SAEED NASSEH  and
RYO TAKAHASHI
SAEED NASSEH
Affiliation:
Department of Mathematical Sciences, Georgia Southern University, Statesboro, Georgia 30460, U.S.A. e-mail: snasseh@georgiasouthern.edu
RYO TAKAHASHI
Affiliation:
Graduate School of Mathematics, Nagoya University, Furocho, Chikusaku, Nagoya, Aichi 464-8602, Japan. e-mail: takahashi@math.nagoya-u.ac.jp
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Abstract

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

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 168 , Issue 2 , March 2020 , pp. 305 - 322
Copyright
Copyright © Cambridge Philosophical Society 2018 

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Footnotes

†

Partly supported by JSPS Grants-in-Aid for Scientific Research 16K05098.

References

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