On $S$-Prime Element Principle
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| 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 |