Work

Locally finite Schreier Varieties

Year: 2026

Type: preprint

Abstract: A variety $\mathcal{V}$ is called a Schreier variety if every subalgebra of a $\mathcal{V}$-free algebra is a $\mathcal{V}$-free algebra. We use ideas from Tame Congruence Theory to classify locally finite Schreier varieties. One version of the classification theorem states that a locally finite variety $\mathcal{V}$ is a Schreier variety if and only if (i) every finite algebra in $\mathcal{V}$ is a $\langle 0,1\rangle$-minimal algebra and (ii) if $\mathcal{V}$ has a constant $1$-ary term operation, then $\mathcal{V}$ also has a constant $0$-ary term operation.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.19651

Authors: Kearnes, Keith A., Moorhead, Andrew, Szendrei, Agnes

Institutions: University of Colorado Boulder, University of Colorado System, Technische Universität Dresden

Language: English

Topic: Advanced Algebra and Logic

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: European Commission

Award: G1304993860

OpenAlex ID: W7213579241

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