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Information × Registration Number 2118U001325, Article popup.category Стаття Title popup.author Fryz Iryna popup.publication 01-01-2018 popup.source_user Донецький національний університет імені Василя Стуса popup.source https://r.donnu.edu.ua/handle/123456789/2376 popup.publisher A REPUBLICII MOLDOVA. BULETINUL ACADEMIEI DE S¸TIINT¸ E Description Article in the journal in BULETINUL ACADEMIEI DE S¸TIINT¸ E A REPUBLICII MOLDOVA. MATEMATICA In this article, we study the connections between orthogonality and retract orthogonality of operations. We prove that if a tuple of operations is retractly orthogonal, then it is orthogonal. However, the 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. popup.nrat_date 2025-01-09 Close