Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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Commun. Korean Math. Soc. 2022; 37(3): 649-658

Online first article October 13, 2021      Printed July 31, 2022

https://doi.org/10.4134/CKMS.c210236

Copyright © The Korean Mathematical Society.

Semi-neutral groupoids and $BCK$-algebras

Hee Sik Kim, Joseph Neggers, Young Joo Seo

Hanyang University; University of Alabama; Daejin University

Abstract

In this paper, we introduce the notion of a left-almost-zero groupoid, and we generalize two axioms which play important roles in the theory of $BCK$-algebra using the notion of a projection. Moreover, we investigate a Smarandache disjointness of semi-leftoids.

Keywords: Left-almost-zero, semi-(neutral, leftoid), power associative, $BCK$-algebra, trace function, projection, Smarandache disjoint

MSC numbers: Primary 20N02, 06F35

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