Modal Operators on RM Algebras.

We consider some generalizations of BCK algebras such as for example RM, tRM, aRM (= BH) algebras and others. We investigate modal operators on such algebras. In particular, we show that the composition of two modal operators on an aRM algebra verifying the transitivity property is also a modal operator if and only if they commute. It is also proved that if two modal operators on an aRM algebra have the same image, then they coincide. Moreover, we introduce and study modal RM algebras. We define modal upper sets of RM algebras and we investigate some properties of these sets. We construct quotient modal RM algebras and we prove that if φ is a homomorphism of a modal RM algebra A onto a modal aRM algebra B, then A/Ker(φ) is isomorphic to B. Furthermore, we establish connections between deductive systems and congruences for modal RM algebras. [ABSTRACT FROM AUTHOR]