Selected Properties of Some Generalizations of BCK Algebras

Abstract

The notion of a RM algebra, introduced recently, is a generalization of many other algebras of logic. The class of RM algebras contains (weak-)BCC algebras, BCH algebras, BCI algebras, BCK algebras and many others. A RM algebra is an algebra A = (A; →, 1) of type (2, 0) satisfying the identities: x → x = 1 and 1 → x = x. In this paper we study the set of maximal elements of a RM algebra, branches of a RM algebra and moreover translation deductive systems of a RM algebra giving so called the Representation Theorem for RM algebras.

Keywords

• rm algebra
• deductive system
• 03g25
• 06f35