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Tropical ideals
| Content Provider | Scilit |
|---|---|
| Author | Maclagan, Diane Rincón, Felipe |
| Copyright Year | 2018 |
| Description | Journal: Compositio Mathematica We introduce and study a special class of ideals, called tropical ideals, in the semiring of tropical polynomials, with the goal of developing a useful and solid algebraic foundation for tropical geometry. The class of tropical ideals strictly includes the tropicalizations of classical ideals, and allows us to define subschemes of tropical toric varieties, generalizing Giansiracusa and Giansiracusa [Equations of tropical varieties, Duke Math. J. 165 (2016), 3379–3433]. We investigate some of the basic structure of tropical ideals, and show that they satisfy many desirable properties that mimic the classical setup. In particular, every tropical ideal has an associated variety, which we prove is always a finite polyhedral complex. In addition we show that tropical ideals satisfy the ascending chain condition, even though they are typically not finitely generated, and also the weak Nullstellensatz. |
| Ending Page | 670 |
| Starting Page | 640 |
| ISSN | 00221295 |
| e-ISSN | 15705846 |
| DOI | 10.1112/s0010437x17008004 |
| Journal | Compositio Mathematica |
| Issue Number | 3 |
| Volume Number | 154 |
| Language | English |
| Publisher | Wiley-Blackwell |
| Publisher Date | 2018-03-01 |
| Access Restriction | Open |
| Subject Keyword | Journal: Compositio Mathematica Weak Nullstellensatz |
| Content Type | Text |
| Resource Type | Article |
| Subject | Algebra and Number Theory |
