Vinayak Joshi

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20212026

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math.AC2026

On $S$ -prime and $S$ -primary elements in multiplicative lattices

Sachin Sarode, Chetan Patil, Vinayak Joshi

In this paper, we study $S$ -prime elements and $S$ -primary elements within the framework of multiplicative lattices. Furthermore, we define and explore weakly $S$ -prime elements an…

math.AC2026

On $S$ -Noetherian Lattices

Sachin Sarode, Chetan Patil, Vinayak Joshi

In this paper, we define and study $S$ -Noetherian lattices as a natural generalization of Noetherian rings. We prove that a ring $R$ is $S$ -Noetherian if and only if its ideal latt…

math.AC2026

On $S$ -Prime Element Principle

Sachin Sarode, Chetan Patil, Vinayak Joshi

In this paper, we introduce $S$ -prime elements in $V$ -lattices, where $S$ is a multiplicatively closed subset of a $V$ -lattice $L$ . In addition, we introduce the $S$ -Prime Element…

math.AC2021

$X$ -elements in multiplicative lattices -- A generalization of $J$ -ideals, $n$ -ideals and $r$ -ideals in rings

Sachin Sarode, Vinayak Joshi

In this paper, we introduce a concept of $X$ -element with respect to an $M$ -closed set $X$ in multiplicative lattices and study properties of $X$ -e…

On S-prime and S-primary elements in multiplicative lattices

On S-Noetherian Lattices

On S-Prime Element Principle

X-elements in multiplicative lattices -- A generalization of J-ideals, n-ideals and r-ideals in rings

On $S$ -prime and $S$ -primary elements in multiplicative lattices

On $S$ -Noetherian Lattices

On $S$ -Prime Element Principle

$X$ -elements in multiplicative lattices -- A generalization of $J$ -ideals, $n$ -ideals and $r$ -ideals in rings