A note on k-cyclic modal pseudocomplemented De Morgan algebras

TL;DR

This paper explores the structure and mappings of finite k-cyclic modal pseudocomplemented De Morgan algebras, providing constructions of epimorphisms and finite free algebras, extending existing theoretical frameworks.

Contribution

It introduces methods for constructing epimorphisms and finite free algebras in k-cyclic modal pseudocomplemented De Morgan algebras, generalizing previous results.

Findings

Constructed epimorphisms between finite symmetric and 2-cyclic algebras.

Computed the cardinality of epimorphism sets for finite structures.

Presented finite free algebra constructions within the variety.

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.