A note on k-cyclic modal pseudocomplemented De Morgan algebras

Symmetric and k-cyclic structure of modal pseudocomplemented De Morgan algebras was introduced previously. In this paper, we first present the construction of epimorphisms 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.