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Locally finite Schreier Varieties

  • Keith A. Kearnes
  • Andrew Moorhead
  • Agnes Szendrei
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Abstract

A variety 𝒱 is called a Schreier variety if every subalgebra of a 𝒱-free algebra is a 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 𝒱 is a Schreier variety if and only if (i) every finite algebra in 𝒱 is a ⟨ 0,1⟩-minimal algebra and (ii) if 𝒱 has a constant $1$-ary term operation, then 𝒱 also has a constant $0$-ary term operation.

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Cite

BibTeXRIS
BibTeX
@misc{kearnes2026locally,
  title = {{Locally finite Schreier Varieties}},
  author = {Keith A. Kearnes and Andrew Moorhead and Agnes Szendrei},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.19651},
  eprint = {2609.19651},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.19651},
}
RIS
TY  - UNPB
TI  - Locally finite Schreier Varieties
AU  - Keith A. Kearnes
AU  - Andrew Moorhead
AU  - Agnes Szendrei
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2609.19651
UR  - https://arxiv.org/abs/2609.19651
AB  - A variety 𝒱 is called a Schreier variety if every subalgebra of a 𝒱-free algebra is a 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 𝒱 is a Schreier variety if and only if (i) every finite algebra in 𝒱 is a ⟨ 0,1⟩-minimal algebra and (ii) if 𝒱 has a constant $1$-ary term operation, then 𝒱 also has a constant $0$-ary term operation.
ER  -