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 $ \varphi $, there exists a groupoid such that $ \varphi $ 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.
Citation: Hee Sik Kim, J. Neggers, Sun Shin Ahn. A generalization of identities in groupoids by functions[J]. AIMS Mathematics, 2022, 7(9): 16907-16916. doi: 10.3934/math.2022928
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 $ \varphi $, there exists a groupoid such that $ \varphi $ 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.
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Hee Sik Kim, J. Neggers, Sun Shin Ahn. A generalization of identities in groupoids by functions[J]. AIMS Mathematics, 2022, 7(9): 16907-16916. doi: 10.3934/math.2022928
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