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arXiv · 2309.00478

On when the union of two algebraic sets is algebraic

Erhard Aichinger·Mike Behrisch·Bernardo Rossi
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Abstract

In universal algebraic geometry, an algebra is called an equational domain if the union of two algebraic sets is algebraic. We characterize equational domains, with respect to polynomial equations, inside congruence permutable varieties, and with respect to term equations, among all algebras of size two and all algebras of size three with a cyclic automorphism. Furthermore, for each size at least three, we prove that, modulo term equivalence, there is a continuum of equational domains of that size.

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Erhard Aichinger, Mike Behrisch, Bernardo Rossi. 2023-09-01. On when the union of two algebraic sets is algebraic. https://doi.org/10.1007/s00010-024-01041-9

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