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Preprint Number 2103
2103. Kaique Matias de Andrade Roberto, Hugo Luiz Mariano
On superrings of polynomials and algebraically closed multifields
Submission date: 23 November 2021
The concept of multialgebraic structure -- an algebraic like structure but endowed with multiple valued operations -- has been studied since the 1930's; in particular, the concept of hyperrings was introduced by Krasner in the 1950's. Some general algebraic study has been made on multialgebras: see for instance  and . More recently the notion of multiring have obtained more attention: a multiring is a lax hyperring, satisfying an weak distributive law, but hyperfields and multifields coincide. Multirings has been studied for applications in abstract quadratic forms theory (, ) and tropical geometry (); a more detailed account of variants of concept of polynomials over hyperrings is even more recent (, ). In the present work we start a model-theoretic oriented analysis of multialgebras introducing the class of algebraically closed and providing variant proof of quantifier elimination flavor, based on new results on superring of polynomials ().
Mathematics Subject Classification:
Keywords and phrases: multialgebras; superring of polynomials; algebraically closed multifields.
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