Orthogonality and retract orthogonality of operations
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612.643.5+517.518.36 (1)
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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

Orthogonality and retract orthogonality of operations

CZU: 612.643.5+517.518.36
MSC 2010: 20N05, 05B15.

Pag. 24-32

Fryz Iryna
 
Vasyl Stus Donetsk National University
 
Disponibil în IBN: 26 iulie 2018


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.

Cuvinte-cheie
orthogonality of operations, retract orthogonality of operations, block-wise recursive algorithm, linear operation, central quasigroup.