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Double MSn-algebras and double Kn.m-algebras

Published online by Cambridge University Press:  18 May 2009

M. Sequeira
M. Sequeira
Affiliation:
Dep. Matemática-Fac. Ciéncias LisboaR. Ernesto De Vasconcelos, Bloco Cl 1700 Lisboa, Portugal
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Abstract

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The variety O2 of all algebras (L; ∧, ∨, f, g, 0, 1) of type (2, 2, 1, 1, 0, 0) such that (L; ∧, ∨, f, 0, 1) and (L; ∧, ∨, g, 0, 1) are Ockham algebras is introduced, and, for n, m εℕ, its subvarieties DMSn, of double MSn-algebras, and DKn,m, of double Kn,m-algebras, are considered. It is shown that DKn,m has equationally definable principal congruences: a description of principal congruences on double Kn,m-algebras is given and simplified for double MSn-algebras. A topological duality for O2-algebras is developed and used to determine the subdirectly irreducible algebras in DKn,m and in DMSn. Finally, MSn-algebras which are reduct of a (unique) double MSn-algebra are characterized.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 35 , Issue 2 , May 1993 , pp. 189 - 201
Copyright
Copyright © Glasgow Mathematical Journal Trust 1993

References

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