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Some Special Elements and Pseudo Inverse Functions in Groupoids

Author

Listed:
  • 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)

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.

Suggested Citation

  • Yong Lin Liu & Hee Sik Kim & Joseph Neggers, 2019. "Some Special Elements and Pseudo Inverse Functions in Groupoids," Mathematics, MDPI, vol. 7(2), pages 1-7, February.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:2:p:173-:d:205969
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