Authors: Krapež, Aleksandar 
Title: Weak associativity and quasigroup units
Journal: Publications de l'Institut Mathematique
Volume: 105
Issue: 119
First page: 17
Last page: 24
Issue Date: 1-Jan-2019
Rank: M24
ISSN: 0350-1302
DOI: 10.2298/PIM1919017K
Abstract: 
We investigate a family of identities similar to weak associativity: x(y/y) · z = x · (y/y)z which might imply the existence of the unit in a quasigroup. A partial solution to Krapež, Shcherbacov Problem concerning such identities and consequently to similar well known Belousov's Problem is obtained. Another problem by Krapež and Shcherbacov is solved affirmatively, showing that there are many single identities determining unipotent loops among quasigroups.
Keywords: Loop | quasigroup | Unit | Weak associativity
Publisher: Mathematical Institute of the SASA
Project: Analysis and algebra with applications 

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