Quasigroups, Units and Belousov's Problem # 18

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

Published
2019-06-11
How to Cite
Krapež, A., & Shcherbacov, V. (2019). Quasigroups, Units and Belousov’s Problem # 18. Armenian Journal of Mathematics, 11(9), 1-27. Retrieved from http://armjmath.sci.am/index.php/ajm/article/view/210