A generalization of identities in groupoids by functions-Reference-Cited by-同舟云学术

A generalization of identities in groupoids by functions

Published:2022 Issue:9 Volume:7 Page:16907-16916
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Kim Hee Sik¹,Neggers J.²,Ahn Sun Shin³

Affiliation:

1. Department of Mathematics, Hanyang University, Seoul, 04763, Korea

2. Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, USA

3. Department of Mathematics Education, Dongguk University, Seoul, 04620, Korea

Abstract

<abstract><p>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.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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