PORTUGALIAEMATHEMATICA
Vol. 61, No. 1, pp. 115-122 (2004)
|
|
PORTUGALIAE MATHEMATICA Vol. 61, No. 1, pp. 115-122 (2004) |
|
|
Free $Q$-distributive lattice over an $n$-element chainLuiz Monteiro, Manuel Abad and Marta ZanderINMABB-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. Full text of the article:
Electronic version published on: 7 Mar 2008.
© 2004 Sociedade Portuguesa de Matemática
|