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On the difference between `tropical functions' and real-valued functions (1507.00545v2)
Published 2 Jul 2015 in math.AC and math.AG
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.