Lattices of classes of groupoids with one-sided quasigroup conditions

Jan Galuszka

Abstract


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.


Keywords


Groupoid, quasigroup, right quasigroup, left quasigroup, Steinitz numbers

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