Year: 2026
Type: preprint
Abstract: The equational probabilistic spectrum of a finite algebra is the set of probabilities with which equations are satisfied in the algebra. We study algebras with minimal spectrum, that is, spectra consisting only of the values $1$ and $1/|\A|$. We show that, apart from trivial cases, groupoids with minimal spectrum are quasigroups. We further prove that several weak associativity conditions collapse into full associativity, and hence into group structure. Finally, we obtain a complete classification of semigroups with minimal spectrum.
Source: arXiv (Cornell University)
Author: Cardó, Carles
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7140079025
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