2025/12/17 by Singh, Tushar, Ansari, Ajim Uddin, Kumar, Shiv Datt
Mathematics · Decision Sciences · #Commutative Algebra and Its Applications #Rings, Modules, and Algebras #Fuzzy and Soft Set Theory
paper · doi:10.48550/arxiv.2512.15078
Let R be a commutative ring with identity, S⊆ 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.