Generic multiplicative endomorphism of a field

Christian d'Elbée

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arXiv · 2212.02115

Generic multiplicative endomorphism of a field

Christian d'Elbée

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Abstract

We introduce the model-companion of the theory of fields expanded by a unary function for a multiplicative map, which we call ACFH. Among others, we prove that this theory is NSOP$_1$ and not simple, that the kernel of the map is a generic pseudo-finite abelian group. We also prove that if forking satisfies existence, then ACFH has elimination of imaginaries.

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BibTeX RIS

Christian d'Elbée. 2025-01-17. Generic multiplicative endomorphism of a field. https://arxiv.org/abs/2212.02115

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