Naturally dualizable algebras omitting types 1 and 5 have a cube term
Rings and Algebras
2019-06-07 v2 Logic
Abstract
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 V(A) is congruence distributive and A is dualizable, then 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 A omits tame congruence types 1 and 5 (all locally finite CM varieties omit these types) and is dualizable, then A has a cube term.
Keywords
Cite
@article{arxiv.1403.7677,
title = {Naturally dualizable algebras omitting types 1 and 5 have a cube term},
author = {Matthew Moore},
journal= {arXiv preprint arXiv:1403.7677},
year = {2019}
}