Analogues of Gluskin–Hosszú and Malyshev theorems for strongly dependent n-ary operations
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Aleksandr V. Cheremushkin
Abstract
The paper contains an extension of Malyshev theorem for n-ary quasigroups with a right or left weak invertibility property to the case of strongly dependent n-ary operations. As a corollary a new proof of Gluskin–Hosszú theorem for strongly dependent n-ary semigroups is obtained.
Originally published in Diskretnaya Matematika (2018) 30, №2, 138–147 (in Russian).
References
[1] Sokhatsky F.N., “On the associativity of multiplace operations”, Diskretnaya matematika, 4:1 (1992), 66–84 (in Russian).Suche in Google Scholar
[2] Gal’fmak A. M., Vorob’yev G.N., “On the Post-Gluskin-Hosszu theorem”, Problemy fiziki, matematiki i tekhniki, 2013, No1(14), 55–59 (in Russian).Suche in Google Scholar
[3] Malyshev F. M., “The Post-Gluskin-Hosszu theorem for finite n-quasigroups and self-invariant families of permutations”, Sb. Math., 207:2 (2016), 226–237.10.1070/SM8447Suche in Google Scholar
[4] Malyshev F. M., “The Post-Gluskin-Hosszú theorem for finite n-quasigroups”, XIV Int. Conf. Algebra and number theory: recent problems and applications, devoted to . 70th anniversary of the birth of G. I. Arkhipova and S. M. Voronina, Issled. poalgebre, teorii chisel, funkts. analizu i smezhnym voprosam: mezhvuz. sb. nauch. tr., 8, Saratov : Izd-vo Sarat. un-ta, 2016, 59–62 (in Russian).Suche in Google Scholar
[5] Sokhatsky F.N., “Generalization of two Belousov theorems for strongly dependent functions of k-valued logic”, Matematicheskie issledovaniya, 1985, No83, 105–115 (in Russian).Suche in Google Scholar
[6] Belousov V. D., n-ary quasigroups, Kishinev: Shtiintsa, 1972 (in Russian), 277 pp.Suche in Google Scholar
[7] Cheremushkin A. V., “Iteration-free decomposition of strongly dependent functions”, DiscreteMath. Appl., 14:5 (2004), 439–478.10.1515/1569392042572159Suche in Google Scholar
© 2019 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- On closed classes in partial k-valued logic that contain the class of monotone functions
- On relationship between the parameters characterizing nonlinearity and nonhomomorphy of vector spaces transformation
- Analogues of Gluskin–Hosszú and Malyshev theorems for strongly dependent n-ary operations
- Generation of the alternating group by modular additions
- Formulas for a characteristic of spheres and balls in binary high-dimensional spaces
- Short single tests for circuits with arbitrary stuck-at faults at outputs of gates
- Bounds on the frequencies of tuples on parts of the period of linear recurring sequences over Galois rings
- Compositions of a numerical semigroup
Artikel in diesem Heft
- Frontmatter
- On closed classes in partial k-valued logic that contain the class of monotone functions
- On relationship between the parameters characterizing nonlinearity and nonhomomorphy of vector spaces transformation
- Analogues of Gluskin–Hosszú and Malyshev theorems for strongly dependent n-ary operations
- Generation of the alternating group by modular additions
- Formulas for a characteristic of spheres and balls in binary high-dimensional spaces
- Short single tests for circuits with arbitrary stuck-at faults at outputs of gates
- Bounds on the frequencies of tuples on parts of the period of linear recurring sequences over Galois rings
- Compositions of a numerical semigroup
