SEMIGROUP DISTANCES OF FINITE GROUPOIDS

Authors

  • Barbora Batíková Czech University of Life Sciences - Department of Mathematics
  • Šárka Dvořáková Czech University of Life Sciences - Department of Mathematics
  • Milan Trch Czech University of Life Sciences - Department of Mathematics

Keywords:

groupoid, non-associative triple, distance of groupoids, semigroup distance

Abstract

The simplest cases of non-associative groupoids are presented by groupoids (so called SH-groupoids) having just one non-associative (ordered) triple of elements.  In this paper, only SH-groupoids having the simplest possible non-associative triple (a, a, a) are investigated.  For each positive integer n finite SH-groupoids En(·) generated by at most two elements are constructed and their semigroup distances are described.  It is proved that there are finite non-associative groupoids having their semigroup distance equal just to the arbitrary given positive integer n.

Cover of n°32 Italian Journal of Pure and Applied Mathematics

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Published

2014-08-22

How to Cite

Batíková, B., Dvořáková, Šárka, & Trch, M. (2014). SEMIGROUP DISTANCES OF FINITE GROUPOIDS. Italian Journal of Pure and Applied Mathematics, 32, 547–560. Retrieved from https://journals.uniurb.it/index.php/ijpam/article/view/6174

Issue

N°32 - August 2014

Section

Articoli - Forum Editrice

License

Copyright (c) 2014 Barbora Batíková, Šárka Dvořáková, Milan Trch

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

L'opera è pubblicata sotto  Licenza Creative Commons Attribuzione 4.0 Internazionale (CC-BY)

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