RM ALGEBRAS AND COMMUTATIVE MOONS

Year 2021, Volume: 29 Issue: 29, 95 - 106, 05.01.2021

Andrzej Walendzıak

https://doi.org/10.24330/ieja.852024

Cited By: 1

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.

Keywords

RM, BH, CI, BCH, BCI algebra, moon, p-semisimplicity

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