The author constructs a three-valued Lukasiewicz-Moisil algebra from a monadic threevalued Lukasiewicz-Moisil algebra, gneralizing A. Monteiro's (1974) construction of a threevalued Lukasiewicz-Moisil algebra from a monadic Boolean algebra, and constructs a rnonadic three-valued Lukasiewicz-Moisil algebra from a monadic n-valued one, generalizing V. Boicescu's (1971) construction of a three-valued Lukasiewicz-Moisil algebra from an n-valued one, n t> 3. Thus one can construct a three-valued Lukasiewicz-Moisil algebra from a monadic n-valued Lukasiewicz-Moisil algebra, n ~> 2.
In~oduction
The notion of a three-valued Lukasiewicz algebra has been introduced by . He has also introduced the notion of an n-valued Lukasiewicz algebra [9], called therefore, by Cignoli [12], a Moisil algebra of order n.
A. Monteiro [1] has found a construction ~ of a three-valued Lukasiewicz-Moisil algebra from a monadic Boolean algebra, using the theory of N-lattices (Nelson algebras). L. Monteiro and Coppola [5] give a direct proof of the result obtained in [1]. A. Monteiro [1] and L. Monteiro [13] have also proved that, given a three-valued Lukasiewicz-Moisil algebra L, there exists a monadic Boolean algebra A such that .~(A), the three-valued Lukasiewicz-Moisil algebra obtained from A by the construction ~, is isomorphic with L.
Boicescu [3,4] gives some constructions of a three-valued Lukasiewicz-Moisil algebra from an n-valued Lukasiewicz-Moisil algebra.
In Section 1 we give a construction ~' of a three-valued Lukasiewicz-Moisil algebra from a monadic three-valued Lukasiewicz-Moisil algebra, generalizing the construction from [5]. In Section 2 we give some constructions of a monadic three-valued Lukasiewicz-Moisil algebra from a monadic n-valued Lukasiewicz-Moisil algebra, extending the results from [3,4] to monadic algebras.