On strong subalgebras of RM algebras

Abstract

The notion of an RM algebra is a generalization of many other algebras of logic. The class of RM algebras contains, for example, BE and BCK algebras. In this paper, there are studied strong subalgebras of an RM algebra. Among other things there is shown that in an RM algebra any strong subalgebra is a subalgebra, the intersection and the union of any strong subalgebras are still strong subalgebras and the set of all strong subalgebras is a complete distributive lattice. Moreover, characterizations of BE algebras in the class of RME algebras and BCK algebras in the class of BCI algebras are also given.