TY - JOUR
T1 - Local rings with quasi-decomposable maximal ideal
AU - Nasseh, Saeed
AU - Takahashi, Ryo
N1 - Publisher Copyright:
Copyright © Cambridge Philosophical Society 2018.
PY - 2020/3/1
Y1 - 2020/3/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85054981480&partnerID=8YFLogxK
U2 - 10.1017/S0305004118000695
DO - 10.1017/S0305004118000695
M3 - Article
AN - SCOPUS:85054981480
SN - 0305-0041
VL - 168
SP - 305
EP - 322
JO - Mathematical Proceedings of the Cambridge Philosophical Society
JF - Mathematical Proceedings of the Cambridge Philosophical Society
IS - 2
ER -