Lattices of classes of groupoids with one-sided quasigroup conditions

• Published in: Algebra and Discrete Mathematics
• Date: 2010
• Main Author: Galuszka, J.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2010
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/154803
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Lattices of classes of groupoids with one-sided quasigroup conditions / J. Galuszka// Algebra and Discrete Mathematics. — 2010. — Vol. 9, № 1. — С. 31–40. — Бібліогр.: 13 назв. — англ.

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.