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Preprint Number 656

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656. Ralph McKenzie and Matthew Smedberg
Strong solvability and residual finiteness for finitely decidable varieties

Submission date: 12 November 2013.


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.

Mathematics Subject Classification: 03D35, 08B26

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Full text arXiv 1311.2683: pdf, ps.

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