Strong solvability and residual finiteness for finitely decidable varieties

Ralph McKenzie; Matthew Smedberg

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arXiv · 1311.2683

Strong solvability and residual finiteness for finitely decidable varieties

Ralph McKenzie·Matthew Smedberg

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Abstract

If V is a finitely generated variety such that the first-order theory of the finite members of V is decidable, we show that V is residually finite, and in fact has a finite bound on the sizes of subdirectly irreducible algebras. This result generalizes known results which assumed that V has modular congruence lattices. Our proof of the theorem in its full generality proceeds by showing that strongly solvable radicals of algebras in V are strongly abelian.

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BibTeX RIS

Ralph McKenzie, Matthew Smedberg. 2013-11-12. Strong solvability and residual finiteness for finitely decidable varieties. https://arxiv.org/abs/1311.2683

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