Lattices of classes of groupoids with one-sided quasigroup conditions

• Date: 2018
• Main Author: Galuszka, Jan
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: Groupoid; quasigroup; right quasigroup; left quasigroup; Steinitz numbers; 05B15; 08A30; 08A40; 08A62; 08A99; 14R10; 20N02; 20N05
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/620
• Journal Title: 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.