Tight closure in non-equidimensional rings
| dc.creator | Singh, Anurag K. | |
| dc.date | 2002-09-18 | |
| dc.date.accessioned | 2026-07-07T04:51:00Z | |
| dc.date.available | 2026-07-07T04:51:00Z | |
| dc.description | An equidimensional local ring is F-rational if and only if one ideal generated by a system of parameters is tightly closed. The question of whether a non-equidimensional local ring can have a tightly closed ideal generated by a system of parameters has been a long-standing open problem, and for certain classes of non-equidimensional rings we prove that this is not possible. A key point is that tight closure has a colon capturing property in equidimensional rings that it does not have in non-equidimensional rings. We define a new closure operation, one that rectifies the absence of the colon capturing property of tight closure in non-equidimensional rings. This closure operation agrees with tight closure when the ring is equidimensional, and we prove that the F-rationality of a local ring is equivalent to a single system of parameters being closed with respect to this new closure operation. | |
| dc.identifier | https://arxiv.org/abs/math/0209236 | |
| dc.identifier | http://arxiv.org/abs/math/0209236 | |
| dc.identifier | Communications in Algebra {\bf 26} (1998) 3969--3983 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64994 | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13A35; 13H10 | |
| dc.title | Tight closure in non-equidimensional rings | |
| dc.type | text |