2021/11/23 by Roberto, Kaique Matias de Andrade, Mariano, Hugo Luiz
#Commutative Algebra (math.AC) #FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.2111.12195
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 \citegolzio2018brief and \citepelea2006multialgebras. 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 (\citemarshall2006real, \citeworytkiewiczwitt2020witt) and tropical geometry (\citejun2015algebraic); a more detailed account of variants of concept of polynomials over hyperrings is even more recent (\citejun2015algebraic, \citeameri2019superring). 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 (\citeameri2019superring).