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A Subalgebra Intersection Property for Congruence Distributive Varieties

Published:2009-04-01
Printed: Apr 2009
• Matthew A. Valeriote
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Abstract

We prove that if a finite algebra $\m a$ generates a congruence distributive variety, then the subalgebras of the powers of $\m a$ satisfy a certain kind of intersection property that fails for finite idempotent algebras that locally exhibit affine or unary behaviour. We demonstrate a connection between this property and the constraint satisfaction problem.
 Keywords: congruence distributive, constraint satisfaction problem, tame congruence theory, \jon terms, Mal'cev condition
 MSC Classifications: 08B10 - Congruence modularity, congruence distributivity 68Q25 - Analysis of algorithms and problem complexity [See also 68W40] 08B05 - Equational logic, Mal'cev (Mal'tsev) conditions

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