Dualizability of automatic algebras

Bentz, W.; Davey, B.A.; Pitkethly, J.G.; Willard, R.

Abstract

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 dualizable if its letters act as an abelian group of permutations on its states. To illustrate the potential difficulty of the general problem, we exhibit an infinite ascending chain of finite automatic algebras that are alternately dualizable and non-dualizable.

Citation

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

• Journal Article Type: Article
• Acceptance Date: Feb 2, 2013
• Online Publication Date: Nov 19, 2013
• Publication Date: Jul 1, 2014
• Deposit Date: Jun 29, 2018
• Journal: Journal of Pure and Applied Algebra
• Print ISSN: 0022-4049
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 218
• Issue: 7
• Pages: 1324-1345
• DOI: https://doi.org/10.1016/j.jpaa.2013.11.020
• Public URL: https://hull-repository.worktribe.com/output/901243
• Publisher URL: https://www.sciencedirect.com/science/article/pii/S0022404913002247?via%3Dihub
• Additional Information: This article is maintained by: Elsevier; Article Title: Dualizability of automatic algebras; Journal Title: Journal of Pure and Applied Algebra; CrossRef DOI link to publisher maintained version: http://dx.doi.org/10.1016/j.jpaa.2013.11.020; Content Type: article; Copyright: Copyright © 2013 Elsevier B.V. All rights reserved.
• Contract Date: Jun 29, 2018