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.
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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}
}
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18 pages