Tight Closure of Finite Length Modules in Graded Rings

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dc.creatorDietz, Geoffrey D.
dc.date2005-08-18
dc.date2007-01-11
dc.date.accessioned2026-07-07T07:39:39Z
dc.date.available2026-07-07T07:39:39Z
dc.descriptionWe look at how the equivalence of tight closure and plus closure (or Frobenius closure) in the homogeneous m-coprimary case implies the same closure equivalence in the non-homogeneous m-coprimary case in standard graded rings. Although our result does not depend upon dimension, the primary application is based on results known in dimension 2 due to the recent results of H. Brenner. We also show that unlike the Noetherian case, the injective hull of the residue field over $R^+$ or $R^\infty$ contains elements that are not killed by any power of the maximal ideal of R.
dc.description14 pages, minor revisions made
dc.identifierhttps://arxiv.org/abs/math/0508357
dc.identifierhttp://arxiv.org/abs/math/0508357
dc.identifierJournal of Algebra, 306 (2006), No. 2, 520--534
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/121531
dc.subjectCommutative Algebra
dc.subject13A35 (Primary) 13B22, 13C11 (Secondary)
dc.titleTight Closure of Finite Length Modules in Graded Rings
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