Asymptotic sequences and rees rings

AbstractLet b1, …, bs be an asymptotic sequence over an ideal I in a Noetherian ring R and let Bi = (b1, …, bi)R. Then it is shown that certain sequences closely related to these elements are asymptotic sequences over R(R,Bi), over tIR(R,I) and over uR(R,I) where R(R,J) is the Rees ring of R with respect to the ideal J. These results then imply that certain other sequences are asymptotic sequences over the corresponding ideals in the associated graded rings and in the monadic transformation rings. As an application of the results, it is shown that if R is local, then each permutation of b1, …, bs is an asymptotic sequence over I and that b1, …, bs are an asymptotic sequence in R