Varieties of prime tropical ideals and the dimension of the coordinate semiring
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915685077090304 |
|---|---|
| author | Joó, Dániel Mincheva, Kalina |
| author_facet | Joó, Dániel Mincheva, Kalina |
| contents | In this note we study the relationship between ideals and congruences of the tropical polynomial and Laurent polynomial semirings. We show that the variety of a non-zero prime ideal of the tropical (Laurent) polynomial semiring consists of at most one point. We also prove a result relating the dimension of an affine tropical variety and the dimension of its coordinate semiring. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_18053 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Varieties of prime tropical ideals and the dimension of the coordinate semiring Joó, Dániel Mincheva, Kalina Algebraic Geometry Commutative Algebra 14T10 (Primary), 16Y60 (Primary), 12K10 (Secondary) In this note we study the relationship between ideals and congruences of the tropical polynomial and Laurent polynomial semirings. We show that the variety of a non-zero prime ideal of the tropical (Laurent) polynomial semiring consists of at most one point. We also prove a result relating the dimension of an affine tropical variety and the dimension of its coordinate semiring. |
| title | Varieties of prime tropical ideals and the dimension of the coordinate semiring |
| topic | Algebraic Geometry Commutative Algebra 14T10 (Primary), 16Y60 (Primary), 12K10 (Secondary) |
| url | https://arxiv.org/abs/2501.18053 |