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arXiv · 2609.25823

The finite basis problem for all subvarieties of the variety $\mathsf{V}(S^0_7)$

Mengya Yue
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Abstract

We solve the finite basis problem for all subvarieties of $\mathsf{V}(S^0_7)$. By considering their intersections with $\mathsf{V}(S_7)$, we reduce the problem to six intervals. We show that $\mathsf{V}(S_7^0)$ has exactly fifteen finitely based subvarieties and that every other subvariety is nonfinitely based. Moreover, $\mathsf{V}(S_c(abc))$ and $\mathsf{V}(SR_6)$ are the only limit subvarieties of $\mathsf{V}(S_7^0)$.

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Mengya Yue. 2026-09-22. The finite basis problem for all subvarieties of the variety $\mathsf{V}(S^0_7)$. https://arxiv.org/abs/2609.25823

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