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arXiv · 2105.09520

Nullstellensatz for relative existentially closed groups

Mohammad Shahryari
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Abstract

We prove that in every variety of $G$-groups, every $G$-existentially closed element satisfies nullstellensatz for finite consistent systems of equations. This will generalize {\bf Theorem G} of \cite{BMR1}. As a result we see that every pair of $G$-existentially closed elements in an arbitrary variety of $G$-groups generate the same quasi-variety and if both of them are $q_{\omega}$-compact, they are geometrically equivalent.

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Mohammad Shahryari. 2021-05-20. Nullstellensatz for relative existentially closed groups. https://arxiv.org/abs/2105.09520

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