Graded annihilators of modules over the Frobenius skew polynomial ring, and tight closure
| dc.creator | Sharp, Rodney Y. | |
| dc.date | 2006-05-12 | |
| dc.date.accessioned | 2026-07-07T07:14:10Z | |
| dc.date.available | 2026-07-07T07:14:10Z | |
| dc.description | This paper is concerned with the tight closure of an ideal in a commutative Noetherian local ring $R$ of prime characteristic $p$. Several authors, including R. Fedder, K.-i. Watanabe, K. E. Smith, N. Hara and F. Enescu, have used the natural Frobenius action on the top local cohomology module of such an $R$ to good effect in the study of tight closure, and this paper uses that device. The main part of the paper develops a theory of what are here called 'special annihilator submodules' of a left module over the Frobenius skew polynomial ring associated to $R$; this theory is then applied in the later sections of the paper to the top local cohomology module of $R$ and used to show that, if $R$ is Cohen--Macaulay, then it must have a weak parameter test element, even if it is not excellent. | |
| dc.description | This is to appear in the Transactions of the American Mathematical Society | |
| dc.identifier | https://arxiv.org/abs/math/0605329 | |
| dc.identifier | http://arxiv.org/abs/math/0605329 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/112763 | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13A35, 16S36, 13D45, 13E05, 13E10 (Primary) 13H10 (Secondary) | |
| dc.title | Graded annihilators of modules over the Frobenius skew polynomial ring, and tight closure | |
| dc.type | text |