Shiv Datt Kumar

activity

20242026

collaborators

5 papers

math.AC2026

On Z-Noetherian Rings

Ambar Dubey, Tushar Singh, Shiv Datt Kumar

In this paper, introduce a new finiteness condition for commutative rings, called $Z$ -Noetherian, under which every ideal contained in the set of zero-divisors $Z (R)$ is finitely g…

math.AC2025

On S-Integral Domains and S-Version of Krull Intersection Theorem

Tushar Singh, Gyanendra K. Verma, Shiv Datt Kumar

Let $S \subseteq R$ be a multiplicatively closed subset of a ring $R$ . We extend several results on integral domains to their $S$ -versions and establish the $S$ -version of Krull int…

math.AC2025

Structural Analysis of Commutative S-Reduced Rings

Tushar Singh, Shiv Datt Kumar

Let $R$ be a commutative ring with identity, $S \subseteq R$ be a multiplicative set. In this paper, we establish that the intersection of all $S$ -prime ideals in an $S$ -reduced ri…

math.AC2025

On S-J-Noetherian Rings

Tushar Singh, Ajim Uddin Ansari, Shiv Datt Kumar

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,…

math.AC2024

A Study of S-Primary Decompositions

Tushar Singh, Ajim Uddin Ansari, Shiv Datt Kumar

Let $R$ be a commutative ring with identity and $S \subseteq R$ be a multiplicative set. An ideal $Q$ of $R$ (disjoint from $S$ ) is said to be $S$ -primary if there exists an $s\in…