Portugaliae Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
Vol. 61, No. 1, pp. 115-122 (2004)

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Free $Q$-distributive lattice over an $n$-element chain

Luiz Monteiro, Manuel Abad and Marta Zander

INMABB-CONICET and Departamento de Matemática,
Universidad Nacional del Sur -- ARGENTINA
E-mail: luizmont@criba.edu.ar , imabad@criba.edu.ar , mzander@criba.edu.ar

Abstract: In this note we provide an explicit construction of $FQ({\bf n})$, the free $Q$-distributive lattice over an $n$-element chain, different from those given by Cignoli [4] and Abad--Díaz Varela [1], and prove that $FQ({\bf n})$ can be endowed with a structure of a De Morgan algebra.

Keywords: ordered sets; $Q$-distributive lattices; free algebras; De Morgan algebras.

Classification (MSC2000): 08B20 06D99, 06D30.

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Electronic version published on: 7 Mar 2008.

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