Graded annihilators of modules over the Frobenius skew polynomial ring, and tight closure

dc.creatorSharp, Rodney Y.
dc.date2006-05-12
dc.date.accessioned2026-07-07T07:14:10Z
dc.date.available2026-07-07T07:14:10Z
dc.descriptionThis 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.descriptionThis is to appear in the Transactions of the American Mathematical Society
dc.identifierhttps://arxiv.org/abs/math/0605329
dc.identifierhttp://arxiv.org/abs/math/0605329
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/112763
dc.subjectCommutative Algebra
dc.subject13A35, 16S36, 13D45, 13E05, 13E10 (Primary) 13H10 (Secondary)
dc.titleGraded annihilators of modules over the Frobenius skew polynomial ring, and tight closure
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