Colloquium Mathematicum, ( ISI ), No (109), Year (2007-3) , Pages (1-7)

Title : ON THE UNIGORM BEHAVIOUR OF THE FROBENIUS CLOSURES OF IDEALS ( On the uniform behaviour of the Frobenius closures of ideals )

Authors: Kazem Khashyarmanesh ,

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Abstract: Let a be a proper ideal of a commutative Noetherian ring R of prime characteristic p and let Q(a) be the smallest positive integer m such that (aF)[pm]=a[pm], where aF is the Frobenius closure of a. This paper is concerned with the question whether the set {Q(a[pm]):m∈N0} is bounded. We give an affirmative answer in the case that the ideal a is generated by an u.s.d-sequence c1,…,cn for R such that (i) the map R/∑nj=1Rcj→R/∑nj=1Rc2j induced by multiplication by c1…cn is an R-monomorphism; (ii) for all p∈ass(cj1,…,cjn), c1/1,…,cn/1 is a pRp-filter regular sequence for Rp for j∈{1,2}.

Keywords

On the uniform behaviour of the Frobenius closures of
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@article{paperid:203110,
author = {Khashyarmanesh, Kazem},
title = {ON THE UNIGORM BEHAVIOUR OF THE FROBENIUS CLOSURES OF IDEALS},
journal = {Colloquium Mathematicum},
year = {2007},
number = {109},
month = {March},
issn = {0010-1354},
pages = {1--7},
numpages = {6},
keywords = {On the uniform behaviour of the Frobenius closures of ideals},
}

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%0 Journal Article
%T ON THE UNIGORM BEHAVIOUR OF THE FROBENIUS CLOSURES OF IDEALS
%A Khashyarmanesh, Kazem
%J Colloquium Mathematicum
%@ 0010-1354
%D 2007

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