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Semiring systems arising from hyperrings

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arxiv 2207.06739 v2 pith:7G2A7ZZ6 submitted 2022-07-14 math.RA

Marianne Akian , Stephane Gaubert , Louis Rowen This is my paper · ORCID
classification math.RA
keywords systemshyperfieldshypersystemsalgebraicarisingconstructionshyperringsapproach
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Hyperfields and systems are two algebraic frameworks which have been developed to provide a unified approach to classical and tropical structures. All hyperfields, and more generally hyperrings, can be represented by systems. Conversely, we show that the systems arising in this way, called {\it hypersystems}, are characterized by certain elimination axioms. Systems are preserved under standard algebraic constructions; for instance matrices and polynomials over hypersystems are systems, but not hypersystems. We illustrate these results by discussing several examples of systems and hyperfields, and constructions like matroids over systems.

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  1. Semirings

    math.RA 2026-02 conditional novelty 5.0 of 10

    Rowen consolidates the pair/surpassing-relation framework that extends classical algebra (roots, matrices, linear algebra, geometry) to semirings without cancellation, adding new root-factor theorems and a map of open...

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