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Quasigroups, Units and Belousov's Problem # 18

Authors

  • Aleksandar Krapež Mathematical Institute of the SASA, Belgrade
  • Victor A. Shcherbacov Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Chisinau

DOI:

https://doi.org/10.52737/18291163-2019.11.9-1-27

Keywords:

Quasigroup, Loop, Unit, Derivative operation, Isotopy

Abstract

We investigate {left, right, middle\} units of quasigroups and families of identities which might imply their existence. A prominent role is played by the newly introduced notion of derivative operation, generalizing Belousov's notions of left/right derivative operations for quasigroups. Partial solutions of the Belousov's Problem # 18 and its generalizations are obtained. Several related problems remain open.

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Published

2019-06-11

Versions

Issue

Vol. 11 No. 9 (2019): Quasigroups, Units and Belousov's Problem # 18

Section

Articles

License

Copyright (c) 2019 Armenian Journal of Mathematics

Creative Commons License

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

How to Cite

Quasigroups, Units and Belousov’s Problem # 18. (2019). Armenian Journal of Mathematics, 11(9), 1-27. http://test.armjmath.sci.am/index.php/ajm/article/view/210