منابع مشابه
Tight Closure in Graded Rings
This paper facilitates the computation of tight closure by giving giving upper and lower bounds on the degrees of elements that need to be checked for inclusion in the tight closure of certain homogeneous ideals in a graded ring. Differential operators are introduced to the study of tight closure, and used to prove that the degree of any element in the tight closure of a homogeneous ideal (but ...
متن کاملTight Closure of Finite Length Modules in Graded Rings
In this article, we 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 work of H. Brenner...
متن کاملTight Closure in Non–equidimensional Rings
Throughout our discussion, all rings are commutative, Noetherian and have an identity element. The notion of the tight closure of an ideal was developed by M. Hochster and C. Huneke in [HH1] and has yielded many elegant and powerful results in commutative algebra. The theory leads to the notion of F–rational rings, defined by R. Fedder and K.-i. Watanabe as rings in which parameter ideals are t...
متن کاملApproximate Roots in Graded Rings
An approximate root of an univariate polynomial over a graded ring A is an element in A for which the evaluated polynomial vanishes up to a prescribed order. We give an algorithm for deciding existence of approximate roots and computing essentially all of them. Based on this algorithm we also suggest a finite representation for multivariate algebraic power series.
متن کاملClosure rings
We consider rings equipped with a closure operation defined in terms of a collection of commuting idempotents, generalising the idea of a topological closure operation defined on a ring of sets. We establish the basic properties of such rings, consider examples and construction methods, and then concentrate on rings which have a closure operation defined in terms of their lattice of central ide...
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ژورنال
عنوان ژورنال: Kyoto Journal of Mathematics
سال: 1997
ISSN: 2156-2261
DOI: 10.1215/kjm/1250518397