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Paper IPM / M / 8550  


Abstract:  
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
(\fraka^{F})^{[pm]}=\fraka^{[pm]}, where \fraka^{F} is
the Frobenius closure of \fraka. This paper is concerned with
the question whether the set {Q(\fraka ^{[pm]}): m ∈ \mathbbN_{0}} is bounded. We give an affirmative answer in the
case that the ideal n is generated by an u.s.dsequence c_{1},... , c_{n} for R such that
(i) the map R/ Σ^{n}_{j=1} Rc_{j}→ R/Σ^{n}_{j=1} Rc_{j}^{2} induced by multiplication by
c_{1},... , c_{n} is an Rmonomorphism;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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