Author:
Kim Hee Sik,Park Choonkil,Shim Eun Hwa
Abstract
<abstract><p>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, $ BCK $-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.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Reference13 articles.
1. O. Borůvka, Foundations of the theory of groupoids and groups, Basel: Springer, 1976. https://doi.org/10.1007/978-3-0348-4121-4
2. R. H. Bruck, A survey of binary systems, 3 Eds., Berlin, Heidelberg: Springer, 1971. https://doi.org/10.1007/978-3-662-43119-1
3. Y. S. Huang, BCI-algebra, Beijing: Science Press, 2006.
4. I. H. Hwang, H. S. Kim, J. Neggers, Some implicativities for groupoids and $BCK$-algebras, Mathematics, 7 (2019), 1–8. https://doi.org/10.3390/math7100973
5. Y. Imai, K. Iséki, On axiom systems of propositional calculi. XIV, Proc. Japan Acad., 42 (1966), 19–22. https://doi.org/10.3792/pja/1195522169