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Paper   IPM / M / 8550
School of Mathematics
  Title:   On the uniform behaviour of the Frobenius closures of ideals
  Author(s):  K. Khashyarmanesh
  Status:   Published
  Journal: Colloq. Math.
  Vol.:  109
  Year:  2007
  Pages:   1-7
  Supported by:  IPM
Let \fraka 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 (\frakaF)[pm]=\fraka[pm], where \frakaF is the Frobenius closure of \fraka. This paper is concerned with the question whether the set {Q(\fraka [pm]): m ∈ \mathbbN0} is bounded. We give an affirmative answer in the case that the ideal n is generated by an u.s.d-sequence c1,... , cn for R such that
(i) the map R/ Σnj=1 RcjRnj=1 Rcj2 induced by multiplication by c1,... , cn is an R-monomorphism;ii) for all ass(c_1^j, ... , c_n^j), c_1/1,...,c_n/1 is a R_−filter regularsequence for R_ for j {1, 2}

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