Equational bases for varieties of Ockham algebras |
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| Authors: | J C Varlet Júlia Vaz de Carvalho |
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| Institution: | (1) Institut de Mathématique, Université de Liège, 12, Grande Traverse – B37, Sart-Tilman, Liège – Belgique , BE;(2) Departamento de Matemática, Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisboa – Portugal e-mail: juliavc@ptmat.lmc.fc.ul.pt, and Centro de álgebra da Universidade de Lisboa, Av. Prof. Gama Pinto, 2, 1649-003 Lisboa – Portugal , PT |
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| Abstract: | We consider the variety O of Ockham algebras and its subvarieties of the form P
m,n
(m > n ≥0), sometimes with an additional condition. We use Priestley duality and a remarkable theorem of Urquhart to develop a simple
method for determining the equational bases of the subvarieties. The axioms that we obtain have the same canonical form and
involve few variables. We illustrate our method by the detailed study of the variety MS
2 and some considerations about P
3,2.
Received July 28, 1998; accepted in final form May 25, 2000. |
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| Keywords: | and phrases:Ockham algebra Priestley duality subdirectly irreducible algebra equational basis tabulation |
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