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On the uniform behaviour of the Frobenius closures of ideals

K. Khashyarmanesh (2007)

Colloquium Mathematicae

Let be a proper ideal of a commutative Noetherian ring R of prime characteristic p and let Q() be the smallest positive integer m such that ( F ) [ p m ] = [ p m ] , where F is the Frobenius closure of . This paper is concerned with the question whether the set Q ( [ p m ] ) : m is bounded. We give an affirmative answer in the case that the ideal is generated by an u.s.d-sequence c₁,..., cₙ for R such that (i) the map R / j = 1 n R c j R / j = 1 n R c ² j induced by multiplication by c₁...cₙ is an R-monomorphism; (ii) for all a s s ( c j , . . . , c j ) , c₁/1,..., cₙ/1 is a R -filter regular sequence...

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