On $S$-Prime Element Principle
Commutative Algebra
2026-04-23 v1
Abstract
In this paper, we introduce -prime elements in -lattices, where is a multiplicatively closed subset of a -lattice . In addition, we introduce the -Prime Element Principle to prove that certain elements in -lattices are -prime elements. This principle leads to a direct and uniform approach to the results on the existence of prime elements in multiplicative lattices when .
Keywords
Cite
@article{arxiv.2604.20820,
title = {On $S$-Prime Element Principle},
author = {Sachin Sarode and Chetan Patil and Vinayak Joshi},
journal= {arXiv preprint arXiv:2604.20820},
year = {2026}
}