On algebraic extensions and algebraic closures of superfields
Commutative Algebra
2023-01-18 v2
Abstract
Building over recent results, we expand the basic theory of algebraic extensions to the realm of superfields -a field with multivalued sum and product-, showing that every superfield has a (unique up to isomorphism) strong algebraic extension to a superfield that is algebraically closed. Moreover we show that every infinite algebraically closed superfield admits quantifier elimination procedure.
Cite
@article{arxiv.2208.08537,
title = {On algebraic extensions and algebraic closures of superfields},
author = {Kaique Matias de Andrade Roberto and Hugo Luiz Mariano and Hugo Rafael de Oliveira Ribeiro},
journal= {arXiv preprint arXiv:2208.08537},
year = {2023}
}