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SM ISO690:2012 FRYZ, Iryna. Orthogonality and retract orthogonality of operations. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2018, vol. 86, nr. 1(86), pp. 24-32. ISSN 1024-7696. |
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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica | |||||
Volumul 86, Numărul 1(86) / 2018 / ISSN 1024-7696 /ISSNe 2587-4322 | |||||
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CZU: 612.643.5+517.518.36 | |||||
MSC 2010: 20N05, 05B15. | |||||
Pag. 24-32 | |||||
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Rezumat | |||||
In this article, we study connections between orthogonality and retract orthogonality of operations. We prove that if a tuple of operations is retractly orthogonal, then it is orthogonal. However, orthogonality of operations doesn’t provide their retract orthogonality. Consequently, every k-tuple of orthogonal k-ary operations is prolongable to a k-tuple of orthogonal n-ary operations. Also, we give some specifications for central quasigroups. In particular for central quasigroups over finite field of prime order, retract orthogonality is the necessary and sufficient condition for orthogonality. The problem of coincidence of orthogonality and retract orthogonality remains open. |
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Cuvinte-cheie orthogonality of operations, retract orthogonality of operations, block-wise recursive algorithm, linear operation, central quasigroup. |
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