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arXiv · 2604.20820

On $S$-Prime Element Principle

Sachin Sarode·Chetan Patil·Vinayak Joshi
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Abstract

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 Principle to prove that certain elements in $V$-lattices are $S$-prime elements. This principle leads to a direct and uniform approach to the results on the existence of prime elements in multiplicative lattices when $S=\{1\}$.

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Sachin Sarode, Chetan Patil, Vinayak Joshi. 2026-04-22. On $S$-Prime Element Principle. https://arxiv.org/abs/2604.20820

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