Local rings with quasi-decomposable maximal ideal
2018 ◽
Vol 168
(2)
◽
pp. 305-322
◽
Keyword(s):
AbstractLet (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.
2016 ◽
Vol 16
(09)
◽
pp. 1750163
Keyword(s):
Keyword(s):
1988 ◽
Vol 104
(3)
◽
pp. 451-478
◽
Keyword(s):
Keyword(s):
2010 ◽
Vol 199
◽
pp. 95-105
◽
Keyword(s):
1975 ◽
Vol 59
◽
pp. 149-152
◽
1989 ◽
Vol 105
(1)
◽
pp. 73-77
◽
2010 ◽
Vol 199
◽
pp. 95-105
◽
Keyword(s):