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| Paper IPM / M / 8550 |
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| Abstract: | |
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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 Rcj→ R/Σnj=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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