Monadic RM Algebras

In this paper we introduce and study the monadic RM algebras. As particular cases we get monadic *RM algebras, monadic RM** algebras, monadic BE algebras, monadic BCI algebras, monadic BCK algebras, etc. The monadic deductive systems and R-congruence relations of a monadic RM algebra are defined and their properties are investigated. For the monadic *RM** algebras, it is proved that there is a one-to-one order-preserving correspondence between the R-congruence relations and the monadic closed t-deductive systems. Finally, we prove that if A is a monadic pre-BBBZ algebra, then the lattice of monadic deductive systems of A is isomorphic to the lattice of the deductive systems of (A(there exists for all), ->, 1), where A(there exists for all) is the set of all fixed elements of A.