On Monadic Operators on Modal Pseudocomplemented De Morgan Algebras and Tetravalent Modal Algebras

Symmetric operators on modal pseudocomplemented De Morgan algebras

“…In what follows, we will study the prime spectrum of a given C k -algebra A with an algebraic technique. First, let us observe the study could be done using topological representation through the techniques given in [16,18]. Proposition 2.5 Let (A, t) be a C k -algebra and U ⊆ A an ultrafilter.…”

“…It is worth mentioning that mpM −algebras constitute a proper subvariety of the variety V 0 studied by H. Sankappanavar in [38]. More recently, the theory of operators over mpM −algebras was considered in [15,16]. In particular, the authors studied the class of mpM −algebras enriched with an automorphism of period 2, this automorphism works as a new unary operator, [16].…”

“…More recently, the theory of operators over mpM −algebras was considered in [15,16]. In particular, the authors studied the class of mpM −algebras enriched with an automorphism of period 2, this automorphism works as a new unary operator, [16].…”

“…One of the principal objects of the present paper is to generalize the work of [16] for an automorphism of period k, where k is a positive integer. This kind of operators was studied over other algebraic strucures, for instance, over Post algebras of order p by López-Martinolich in [32] (see also [33,12]), where the variety of k-cyclic Post algebras of order p was studied.…”

A note on k-cyclic modal pseudocomplemented De Morgan algebras

“…It is worth mentioning that the class of mpM −algebras constitutes a proper subvariety of the variety V 0 studied by H. Sankappanavar in [23]. More recently, the theory of operators over mpM −algebras was considered by Figallo-Orellano et al in [10,11,12]. In particular, they studied the class of mpM −algebras enriched with an automorphism of period 2 and k, where k is an positive integer; in fact, this automorphism works as a new unary operator.…”