Tight closure test exponents for certain parameter ideals
| dc.creator | Sharp, Rodney Y. | |
| dc.date | 2005-08-12 | |
| dc.date.accessioned | 2026-07-07T05:22:19Z | |
| dc.date.available | 2026-07-07T05:22:19Z | |
| dc.description | This paper is concerned with the tight closure of an ideal $I$ in a commutative Noetherian ring $R$ of prime characteristic $p$. The formal definition requires, on the face of things, an infinite number of checks to determine whether or not an element of $R$ belongs to the tight closure of $I$. The situation in this respect is much improved by Hochster's and Huneke's test elements for tight closure, which exist when $R$ is a reduced algebra of finite type over an excellent local ring of characteristic $p$. More recently, Hochster and Huneke have introduced the concept of test exponent for tight closure: existence of these test exponents would mean that one would have to perform just one single check to determine whether or not an element of $R$ belongs to the tight closure of $I$. However, to quote Hochster and Huneke, 'it is not at all clear whether to expect test exponents to exist; roughly speaking, test exponents exist if and only if tight closure commutes with localization'. The main purpose of this paper is to provide a short direct proof that test exponents exist for parameter ideals in a reduced excellent equidimensional local ring of characteristic $p$. | |
| dc.description | This is to appear in the Michigan Mathematical Journal | |
| dc.identifier | https://arxiv.org/abs/math/0508214 | |
| dc.identifier | http://arxiv.org/abs/math/0508214 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76016 | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13A35, 13A15, 13D45, 13E05, 13E10, 13H10, 16S36 (Primary) 13C15 (Secondary) | |
| dc.title | Tight closure test exponents for certain parameter ideals | |
| dc.type | text |