Some Special Elements and Pseudo Inverse Functions in Groupoids

Yong Lin Liu, Hee Sik Kim and Joseph Neggers
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Yong Lin Liu: School of Mathematics and Finance, Putian University, Putian 351100, China
Hee Sik Kim: Research Institute of Natural Sciences, Department of Mathematics, Hanyang University, Seoul 04763, Korea
Joseph Neggers: Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, USA

Mathematics, 2019, vol. 7, issue 2, 1-7

Abstract: In this paper, we consider a theory of elements u of a groupoid ( X , ∗ ) that are associated with certain functions u ^ : X → X , pseudo-inverse functions, which are generalizations of the inverses associated with units of groupoids with identity elements. If classifying the elements u as special of one of twelve types, then it is possible to do a rather detailed analysis of certain cases, leftoids, rightoids and linear groupoids included, which demonstrates that it is possible to develop a successful theory and that a good deal of information has already been obtained with much more possible in the future.

Keywords: (completely) ( LL -) special element; pseudo inverse; linear groupoid (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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