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Hyperidentities with permutations in invertible binary algebras

Authors

  • Davit Shahnazaryan Yerevan State University
  • Sergey Davidov Yerevan State University

DOI:

https://doi.org/10.52737/18291163-2020.12.12-1-21

Keywords:

Invertible algebra, Second-order formula, Hyperidentity with permutations, Isotopy

Abstract

In this paper, using hyperidentities with permutations we obtained characterization invertible algebras of various types of linearity.

References

J. Aczel, Yorlensungen uiber Funktionalgleichungen und ihre Anwendungem, Berlin, VEB Deutsch. Verl.Wiss., 1961.

J. Aczel, V. D. Belousov, M. Hosszu, Generalized associativity and bisymmetry on quasigroups, Acta Math. Acad. Sci. Hung. 11 (1-2), 1960, pp. 127-136.

V. D. Belousov, Balanced identities on quasigroups, Mat. Sb., 70 (112) 1, 1966, pp. 55-97 (Russian).

V. D. Belousov, Foundations of the theory of quasigroups and loops, Nauka, 1967 (Russian).

V. D. Belousov, Globally associative systems of quasigroups, Mat. Sb., 55 (97) 2, 1961, pp. 221-236 (Russian).

G. B. Belyavskaya, A. Kh. Tabarov, Identities with permutations leading to linearity of a quasigroup, Discrete Math. Appl. 19, 2009, 172-190.

S. S. Davidov, A characterization of binary invertible algebras linear over a group, Quasigroups Relat. Syst., 19, 2011, pp. 207-222.

S. S. Davidov, A characterization of binary invertible algebras of various type of linearity, Quasigroups Relat. Syst., 20, 2012, pp. 169-176.

S. S. Davidov, D. A. Shahnazaryan, Hyperidentities with permutations leading to the isotopy of invertible binary algebras to a group, Quasigroups Relat. Syst., 28 (1), 2020, pp. 47-52.

S. S. Davidov, A characterization of invertible algebras linear over a group by second-order formulas, J. Algebra Appl., 16 (11), 2017, pp. 175-238.

Yu. M. Movsisyan, Hyperidentities and related concepts 1, Arm. J. Math., 9 (2), 2017, pp. 146-222.

Yu. M. Movsisyan, Introduction to the theory of algebras with hyperidentities, Yerevan State University press, 1986 (Russian).

Yu. M. Movsisyan, S. S. Davidov, Algebras that are nearly quasigroups, Moscow, URSS, 2018 (Russian).

Yu. M. Movsisyan, Hyperidentities in algebras and varieties, Russian Math. Surveys, 53 (1), 1998, pp. 57-108.

Yu. M. Movsisyan, Biprimitive classes of second order algebras, Mat. Issled., 9, 1974, pp. 70-82 (Russian).

A. Sade, Theorie des systemes demosiens de groupoids, Pacif. J. Math., 10 (2), 1960, pp. 625-660.

R. Schauffler, Die Assoziativit$ddot{a}$t im Ganzen Besonders bei Quasigruppen, Math. Zeitschr., 67 (5), 1957, pp. 428-435.

V.A. Shcherbakov, On linear and inverse quasigroups and their applications in code theory, Dissertation of Doctor of Sciences, 247 pages, 2008.

F.N. Sokhatsky, On isotopes of groups I, Ukr. Math. J., 47 (10), 1995, pp. 1585-1598.

F.N. Sokhatsky, On isotopes of groups II, Ukr. Math. J., 47 (12), 1995, pp. 1935-1948.

F.N. Sokhatsky, On isotopes of groups III, Ukr. Math. J., 48 (2), 1996, pp. 283-293.

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Published

2020-12-29

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How to Cite

Hyperidentities with permutations in invertible binary algebras. (2020). Armenian Journal of Mathematics, 12(12). http://test.armjmath.sci.am/index.php/ajm/article/view/443