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Finite Extensions of $\mathbb{Z}_\mathrm{max}$

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arxiv 1406.1121 v2 pith:GTJA3TO2 submitted 2014-06-04 math.RA

Jeffrey Tolliver This is my paper · ORCID
classification math.RA
keywords mathbbmathrmclassifycontainingdivisionextensionsfinitefinitely
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abstract

We classify the semifields and division semirings containing the max-plus semifield $\mathbb{Z}_\mathrm{max}$, which are finitely generated as $\mathbb{Z}_\mathrm{max}$-semimodules.

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  1. Polynomials over idempotent semifields

    math.AC 2026-07 accept novelty 6.0 of 10

    Closed polynomials over idempotent semifields split into linear factors; algebraically closed means every polynomial is closable, and every complete idempotent semifield is algebraically closed.

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