A note on k-cyclic modal pseudocomplemented De Morgan algebras

Abstract: Symmetric and k-cyclic structure of modal pseudocomplemented De Morgan algebras algebras was introduced previously. In this paper, we first present the construction of epimorphims between finite symmetric (or 2-cyclic) modal pseudocomplemented De Morgan algebras. Furthermore, we compute the cardinality of the set of all epimorphism between finite structures. Secondly, we present the construction of finite free algebras on the variety of k-cyclic modal pseudocomplemented De Morgan algebras and display how our computations are in fact generalizations to others in the literature. Our work is strongly based on the properties of epimorphisms and automorphisms and the fact that the variety is finitely generated.