@article{Kim2022, 
author = {Hee Sik Kim and J. Neggers and Sun Shin Ahn},
title = {A generalization of identities in groupoids by functions},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {9},
pages = {16907-16916},
keywords = {groupoid, (right, left) idenfunction, BCK-algebra, leftoid, right pseudo semigroup, (right, left) inversal},
url = {https://www.sciopen.com/article/10.3934/math.2022928},
doi = {10.3934/math.2022928},
abstract = {In this paper, we introduce the notions of a left and a right idenfunction in a groupoid by using suitable functions, and we apply this concept to several algebraic structures. Especially, we discuss its role in linear groupoids over a field. We show that, given an invertible function    φ, there exists a groupoid such that    φ is a right idenfunction. The notion of a right pseudo semigroup will be discussed in linear groupoids. The notion of an inversal is a generalization of an inverse element, and it will be discussed with idenfunctions in linear groupoids over a field.}
}