On $S$-Prime Element Principle

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Sarode, Sachin, Patil, Chetan, Joshi, Vinayak
Format: Preprint
Published: 2026
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866913055714050048
author Sarode, Sachin
Patil, Chetan
Joshi, Vinayak
author_facet Sarode, Sachin
Patil, Chetan
Joshi, Vinayak
contents 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 $S=\{1\}$.
format Preprint
id arxiv_https___arxiv_org_abs_2604_20820
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle On $S$-Prime Element Principle
Sarode, Sachin
Patil, Chetan
Joshi, Vinayak
Commutative Algebra
Primary 06F10, 13A15, 13C05, Secondary 06A11
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 $S=\{1\}$.
title On $S$-Prime Element Principle
topic Commutative Algebra
Primary 06F10, 13A15, 13C05, Secondary 06A11
url https://arxiv.org/abs/2604.20820