@article{Kim2022, 
author = {Hee Sik Kim and Choonkil Park and Eun Hwa Shim},
title = {Function kernels and divisible groupoids},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {7},
pages = {13563-13572},
keywords = {groupoid, BCK-algebra, φ-kernel, coset, divisible, idenfunction},
url = {https://www.sciopen.com/article/10.3934/math.2022749},
doi = {10.3934/math.2022749},
abstract = {In this paper, we introduce the notion of a function kernel which was motivated from the kernel in group theory, and we apply this notion to several algebraic structures, e.g., groups, groupoids,    B  C  K-algebras, semigroups, leftoids. Using the notions of left and right cosets in groupoids, we investigate some relations with function kernels. Moreover, the notion of an idenfunction in groupoids is introduced, which is a generalization of an identity axiom in algebras by functions, and we discuss it with function kernels.}
}