Algebra universalis

, Volume 75, Issue 2, pp 221–230 | Cite as

Naturally dualizable algebras omitting types 1 and 5 have a cube term

  • Matthew Moore


An early result in the theory of Natural Dualities is that an algebra with a near unanimity (NU) term is dualizable. A converse to this is also true: if \({\mathcal{V}(\mathbb{A})}\) is congruence distributive and \({\mathbb{A}}\) is dualizable, then \({\mathbb{A}}\) has an NU term. An important generalization of the NU term for congruence distributive varieties is the cube term for congruence modular (CM) varieties, and it has been thought that a similar characterization of dualizability for algebras in a CM variety would also hold. We prove that if \({\mathbb{A}}\) omits tame congruence types 1 and 5 (all locally finite CM varieties omit these types) and is dualizable, then \({\mathbb{A}}\) has a cube term.

Keywords and phrases

natural duality congruence modular cube term 

2010 Mathematics Subject Classification

Primary: 08C20 Secondary: 08B10 


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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Vanderbilt UniversityNashvilleU.S.A

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