Let A be a Noetherian ring and I be a nonzero ideal of A. Let  be the generalized Rees ring of the ideal I. Let be a semi-prime operation on the set of ideals of A  The sequence  stabilizes in  for large  enough integers n under certain conditions. We first show in this paper, examples of semi-prime operations  and  such that  for all integers n, and reveal that  when n is large enough in  Finally, we extend these results to filtrations.

Rees ring, closure operation, prime divisors.

Received: December 12, 2023; Revised: February 27, 2024; Accepted: March 15, 2024

How to cite this article: K. A. Essan, Closure operation extended to Rees ring and asymptotic prime divisors, JP Journal of Algebra, Number Theory and Applications 63(4) (2024), 297-311. https://doi.org/10.17654/0972555524018

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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