All Outputs (2)

Dualizability of automatic algebras (2013)
Journal Article
Bentz, W., Davey, B., Pitkethly, J., & Willard, R. (2014). Dualizability of automatic algebras. Journal of pure and applied algebra, 218(7), 1324-1345. https://doi.org/10.1016/j.jpaa.2013.11.020

We make a start on one of George McNulty's Dozen Easy Problems: “Which finite automatic algebras are dualizable?” We give some necessary and some sufficient conditions for dualizability. For example, we prove that a finite automatic algebra is dualiz... Read More about Dualizability of automatic algebras.

Supernilpotence prevents dualizability (2013)
Journal Article
Bentz, W., & Mayr, P. (2014). Supernilpotence prevents dualizability. Journal of the Australian Mathematical Society, 96(01), 1-24. https://doi.org/10.1017/S1446788713000517

We address the question of the dualizability of nilpotent Mal’cev algebras, showing that nilpotent finite Mal’cev algebras with a nonabelian supernilpotent congruence are inherently nondualizable. In particular, finite nilpotent nonabelian Mal’cev al... Read More about Supernilpotence prevents dualizability.