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arXiv · 2510.23647

Coherent Conditions: Algebraic Geometry for Arbitrary Classes of Algebras

K. R. van Nispen
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Abstract

Universal algebraic geometry is generalised from solutions of equations in a single algebra to the study of $\varphi$- or $K$-spectra, akin to the prime spectrum of a ring. We explore their basic properties and constructions, give a correspondence between certain quantifier-free propositions and closed sets in the Zariski topology of a free algebra, and show the connection with current UAG. Lastly, equationally Noetherian classes and irreducible spectra are explored.

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K. R. van Nispen. 2025-10-25. Coherent Conditions: Algebraic Geometry for Arbitrary Classes of Algebras. https://arxiv.org/abs/2510.23647

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