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- W4285596303 abstract "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." @default.
- W4285596303 created "2022-07-16" @default.
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- W4285596303 date "2022-07-14" @default.
- W4285596303 modified "2023-09-25" @default.
- W4285596303 title "Semiring systems arising from hyperrings" @default.
- W4285596303 doi "https://doi.org/10.48550/arxiv.2207.06739" @default.
- W4285596303 hasPublicationYear "2022" @default.
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