Lattices of classes of groupoids with one-sided quasigroup conditions

• Datum: 2018
• 1. Verfasser: Galuszka, Jan
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Lugansk National Taras Shevchenko University 2018
• Schlagworte: Groupoid; quasigroup; right quasigroup; left quasigroup; Steinitz numbers; 05B15; 08A30; 08A40; 08A62; 08A99; 14R10; 20N02; 20N05
• Online Zugang: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/620
• Назва журналу: Algebra and Discrete Mathematics

It is shown that two classes of groupoids satisfying certain one-sided quasigroup conditions, namely the classes of one-sided torsion groupoids and of one-sided finite exponent groupoids, are complete lattices, both isomorphic to the lattice of Steinitz numbers with  the divisibility relation.