English

On the difference between `tropical functions' and real-valued functions

Commutative Algebra 2016-03-08 v2 Algebraic Geometry

Abstract

I introduce the concept of integral closure for elements and ideals in idempotent semirings, and establish how it corresponds to its namesake in commutative algebra. In the case of free semirings, integral closure can be understood in terms of a certain monoid of convex bodies under Minkowski sum. I argue that integral closure therefore accounts for the difference between `tropical functions' and real functions.

Keywords

Cite

@article{arxiv.1507.00545,
  title  = {On the difference between `tropical functions' and real-valued functions},
  author = {Andrew W. Macpherson},
  journal= {arXiv preprint arXiv:1507.00545},
  year   = {2016}
}

Comments

18 pages

R2 v1 2026-06-22T10:04:27.941Z