On S-J-Noetherian Rings

Tushar Singh; Ajim Uddin Ansari; Shiv Datt Kumar

paper

On S-J-Noetherian Rings

arXiv:2512.15078

Abstract

Let $R$ be a commutative ring with identity, $S \subseteq R$ be a multiplicative set and $J$ be an ideal of $R$ . In this paper, we introduce the concept of $S$ - $J$ -Noetherian rings, which generalizes both $J$ -Noetherian rings and $S$ -Noetherian rings. We study several properties and charaterizations of this new class of rings. For instance, we prove Cohen's-type theorem for $S$ - $J$ -Noetherian rings. Among other results, we establish the existence of $S$ -primary decomposition in $S$ - $J$ -Noetherian rings as a generalization of classical Lasker-Noether theorem.