Free Algebras Over a Poset in Varieties of Łukasiewicz–Moisil Algebras

A general construction of the free algebra over a poset in varieties finitely generated is given in [8]. In this paper, we apply this to the varieties of Łukasiewicz-Moisil algebras, giving a detailed description of the free algebra over a finite poset (X, ≤) , Freen((X, ≤)). As a consequence of this description, the cardinality of Freen((X, ≤)). is computed for special posets.