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Semiring Systems Arising from Hyperrings by Akian, Marianne; Gaubert, Stephane; Rowen, Louis is a scholarly article available to read on EtoBox.

What is Semiring Systems Arising from Hyperrings about?

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.

Author

Akian, Marianne; Gaubert, Stephane; Rowen, Louis

Published

2022

Language

EN