English

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.

Keywords

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}
}
R2 v1 2026-06-25T01:46:57.679Z