Article ID Journal Published Year Pages File Type
4596204 Journal of Pure and Applied Algebra 2014 22 Pages PDF
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 A1⩽A2⩽A3⩽⋯ of finite automatic algebras that are alternately dualizable and non-dualizable.
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Physical Sciences and Engineering Mathematics Algebra and Number Theory
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