Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6425031 | Advances in Mathematics | 2016 | 28 Pages |
Abstract
We study how geometric properties of tropical convex sets and polytopes, which are of interest in many application areas, manifest themselves in their algebraic structure as modules over the tropical semiring. Our main results establish a close connection between pure dimension of tropical convex sets, and projectivity (in the sense of ring theory). These results lead to a geometric understanding of idempotency for tropical matrices. As well as their direct interest, our results suggest that there is substantial scope to apply ideas and techniques from abstract algebra (in particular, ring theory) in tropical geometry.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Zur Izhakian, Marianne Johnson, Mark Kambites,