RM ALGEBRAS AND COMMUTATIVE MOONS

Abstract

Some generalizations of BCI algebras (the RM, BH, CI, BCH, BH**, BCH**, and *aRM** algebras) satisfying the identity $(x \rightarrow 1)\rightarrow y = (y \rightarrow 1) \rightarrow x$ are considered. The connections of these algebras and various generalizations of commutative groups (such as, for example, involutive commutative moons and commutative (weakly) goops) are described. In particular, it is proved that an RM algebra verifying this identity is equivalent to an involutive commutative moon.