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Identities with permutations associated with quasigroups isotopic to groups.
Authors: Beliavscaia Galina
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Abstract
In this note we select a class of identities with permutations including three variables in a quasigroup (Q, ·) each of which provides isotopy of this quasigroup to a group and describe a class of identities in a primitive quasigroup (Q, ·, \ , / ) each of which is sufficient for the quasigroup (Q, ·) to be isotopic to a group. From these results it follows that in the identity of V.Belousov [6] characterizing a quasigroup isotopic to a group (to an abelian group) two from five (one of four) variables can be fixed.E-mail:
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Contents
- Properties of accessible subrings of topological rings when taking quotient rings.
- Identities with permutations associated with quasigroups isotopic to groups.
- On natural and conatural sets of left ideals of a ring.
- Locicaly separable algebras in varieties of algebras.
- On definitions of groupoids closely connected with quasigroups.
- Radicals of Morita rings revisited.
- Isomorphism of the factor powers of finite groups.
- On torsionfree LCA groups with commutative rings of continuous endomorphisms.
- Crossed-inverse-property groupoids.
- An abstract approach to the study of derivation mappings on non-commutative rings.
- Quasivarieties of Commutative Solvable Moufang loops.
- On description of some radical filters of noetherian rings.
