On S-J-Noetherian Rings
Commutative Algebra
2025-12-18 v1
Abstract
Let be a commutative ring with identity, be a multiplicative set and be an ideal of . In this paper, we introduce the concept of --Noetherian rings, which generalizes both -Noetherian rings and -Noetherian rings. We study several properties and charaterizations of this new class of rings. For instance, we prove Cohen's-type theorem for --Noetherian rings. Among other results, we establish the existence of -primary decomposition in --Noetherian rings as a generalization of classical Lasker-Noether theorem.
Cite
@article{arxiv.2512.15078,
title = {On S-J-Noetherian Rings},
author = {Tushar Singh and Ajim Uddin Ansari and Shiv Datt Kumar},
journal= {arXiv preprint arXiv:2512.15078},
year = {2025}
}