Սա հնացած տարբերակ է, որը հրապարակվել է 2020-12-29 -ում: Կարդացեք վերջին տարբերակը:

Hyperidentities with permutations in invertible binary algebras

Հեղինակներ

  • Davit Shahnazaryan Երևանի պետական համալսարան image/svg+xml
  • Sergey Davidov Երևանի պետական համալսարան image/svg+xml

DOI:

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

Բանալի բառեր:

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

Ամփոփում

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

Ներբեռնումներ

Ներբեռնման տվյալները դեռ հասանելի չեն:

Հղումներ

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.

Ներբեռնումներ

Հրատարակվել է

2020-12-29

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Ինչպես մեջբերել

[1]
D. Shahnazaryan and S. Davidov, “Hyperidentities with permutations in invertible binary algebras”, Armen.J.Math., vol. 12, no. 12, Dec. 2020, Accessed: May 09, 2026. [Online]. Available: http://test.armjmath.sci.am/index.php/ajm/article/view/443