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IMI/Publicaţii/BASM/Ediţii/BASM n.3 (49), 2005/

On Commutativity and Mediality of Polyagroup Cross Isomorphs.

Authors: F.M. Sokhatsky, O.V. Yurevych

Abstract

The notion of cross isotopy (cross isomorphism) of n-ary operations can be got from the well-known notion of isotopy (isomorphism) by replacing one of its components with a k-ary m-invertible operation [1, 2]. The idea of consideration of cross isotopy belongs to V.D. Belousov [3], who defined it for binary quasigroups. In the paper necessary and sufficient conditions for commutativity and mediality of a polyagroup cross isomorph (when n>2k) are determined. A neutrality criterion of an arbitrary element is stated.

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