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Orthogonality and retract orthogonality of operations
Authors: Iryna Fryz
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Abstract
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.Vasyl’ Stus Donetsk National University
600-richia str. 21
21021 Vinnytsia
Ukraine
E-mail:
600-richia str. 21
21021 Vinnytsia
Ukraine
E-mail:
Fulltext
– 0.13 Mb
Contents
- Shape dimension of maps
- Semi-integral filters and semi-integral BL-algebras
- Orthogonality and retract orthogonality of operations
- An Approach for Determining the Optimal Strategies for an Average Markov Decision Problem with Finite State and Action Spaces
- The Center of the Lattice of Factorization Structures
- Properties of finite unrefinable chains of ring topologies for nilpotent rings
- Quartic differential systems with an invariant straight line of maximal multiplicity
- Distances on Free Semigroups and Their Applications
- Integrability conditions for a class of cubic differential systems with a bundle of two invariant straight lines and one invariant cubic
