Let A be a Noetherian ring, and  be a strongly Noetherian filtration on the ring A. Then we generalize the Artin-Rees Lemma to strongly Noetherian filtrations. This allows us to show that if the ideal I₁ contains an f-superficial element of order one which is regular, then the sequence  stabilizes.

Noetherian ring, filtration, associated prime ideals, superficial element.

Received: January 2, 2025; Revised: February 18, 2025; Accepted: March 10, 2025; Published: March 31, 2025

How to cite this article: N. C. Akaffou, D. Kamano, E. D. Akeke and A. Abdoulaye, Asymptotic stability of  for strongly Noetherian filtration JP Journal of Algebra, Number Theory and Applications 64(3) (2025), 239-250. https://doi.org/10.17654/0972555525014

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

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