On algebraic extensions and algebraic closures of superfields

Kaique Matias de Andrade Roberto; Hugo Luiz Mariano; Hugo Rafael de Oliveira Ribeiro

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arXiv · 2208.08537

On algebraic extensions and algebraic closures of superfields

Kaique Matias de Andrade Roberto·Hugo Luiz Mariano·Hugo Rafael de Oliveira Ribeiro

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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.

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Kaique Matias de Andrade Roberto, Hugo Luiz Mariano, Hugo Rafael de Oliveira Ribeiro. 2022-08-17. On algebraic extensions and algebraic closures of superfields. https://arxiv.org/abs/2208.08537

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