Aldo V. Figallo, Departamento de Matematica, Universidad Nacional del Sur, 8000 Bahia Blanca, Argentina, Instituto de Ciencias Basicas, Universidad Nacional de San Juan, 5400 San Juan, Argentina, e-mail: matfiga@criba.edu.ar; Claudia Sanza, Departamento de Matematica, Universidad Nacional del Sur, 8000 Bahia Blanca, Argentina, e-mail: csanza@criba.edu.ar; Alicia N. Ziliani, Departamento de Matematica, Universidad Nacional del Sur, 8000 Bahia Blanca, Argentina, Instituto de Ciencias Basicas, Universidad Nacional de San Juan, 5400 San Juan, Argentina, e-mail: aziliani@criba.edu.ar
Abstract: Some functional representation theorems for monadic $n$-valued Lukasiewicz algebras (qLk$_n$-algebras, for short) are given. Bearing in mind some of the results established by G. Georgescu and C. Vraciu (Algebre Boole monadice si algebre Lukasiewicz monadice, Studii Cercet. Mat. 23 (1971), 1027-1048) and P. Halmos (Algebraic Logic, Chelsea, New York, 1962), two functional representation theorems for qLk$_n$-algebras are obtained. Besides, rich qLk$_n$-algebras are introduced and characterized. In addition, a third theorem for these algebras is presented and the relationship between the three theorems is shown.
Keywords: monadic $n$-valued Lukasiewicz algebra, monadic Boolean algebra
Classification (MSC 2000): 06D30, 03G20
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