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 SM ISO690:2012SOKHATSKY, Fedir M., YUREVYCH, O.. On Commutativity and Mediality of Polyagroup
Cross Isomorphs. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2005, nr. 3(49), pp. 141-152. ISSN 1024-7696. |
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| Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica | ||||||
| Numărul 3(49) / 2005 / ISSN 1024-7696 /ISSNe 2587-4322 | ||||||
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| Pag. 141-152 | ||||||
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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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| Cuvinte-cheie n-ary quasigroup, cross isomorphism, cross isotopy, (i, j)-associative operation. |
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