Irrelevant prime divisors (Q910435)

Let \(I\subset P\) be ideals in a noetherian ring R, with P a prime ideal and I containing a non-zero divisor [the author calls this a regular ideal, a term not often used in commutative algebra to describe such an ideal]. Let R(I) be the Rees ring, \(R[t^{-1}=u,It]\). The author is interested in the question: when is the ideal (u,P,It) an associated prime of R/uR(I) ? It is proved that if \(P\in Ass(R/I^ n)- Ass(R/I^{n+1})\), then (u,P,It) is an associated prime of R/uR(I). Some of the results in this paper have appeared in a paper by the author and \textit{L. J. Ratliff} jun. [Trans. Am. Math. Soc. 303, 311-324 (1987; Zbl 0628.13003)]. The proofs here are shorter. Also there are more details about an example by R. C. Cowsik, which was alluded to in the above mentioned paper - the full verification details are not written down here (or anywhere else, I believe).