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

Published: 2019-06-11

Articles

  • Articles

    Quasigroups, Units and Belousov's Problem # 18

    Aleksandar Krapež, Victor A. Shcherbacov
    View PDF
    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.

    References