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.
Citation: Hee Sik Kim, Choonkil Park, Eun Hwa Shim. Function kernels and divisible groupoids[J]. AIMS Mathematics, 2022, 7(7): 13563-13572. doi: 10.3934/math.2022749
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.
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Hee Sik Kim, Choonkil Park, Eun Hwa Shim. Function kernels and divisible groupoids[J]. AIMS Mathematics, 2022, 7(7): 13563-13572. doi: 10.3934/math.2022749
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