Affiliation:
1. Department of Mathematics and Computer Science, University of Missouri — St. Louis, 309 CCB, 8001 Natural Bridge Road, St. Louis, MO 63121, USA
Abstract
A ternary algebra is a bounded distributive lattice with additonal operations e and ~ that satisfies (a+b)~=a~b~, a~~=a, e≤a+a~, e~= e and 0~=1. This article characterizes free ternary algebras by giving necessary and sufficient conditions on a set X of free generators of a ternary algebra L, so that X freely generates L. With this characterization, the free ternary algebra on one free generator is displayed. The poset of join irreducibles of finitely generated free ternary algebras is characterized. The uniqueness of the set of free generators and their pseudocomplements is also established.
Publisher
World Scientific Pub Co Pte Lt
Cited by
4 articles.
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