On functional equation of associativity with right quasigroup operations
Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 53 (2019) no. 3, pp. 150-155 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider equations of associativity and transitivity. We obtain necessary conditions for the solution of these equations for right quasigroup operations, generalizing the classical quasigroup case.
Keywords: transitive, isotopic, homotopic, hyperidentity.
Mots-clés : associative
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D. A. Shahnazaryan. On functional equation of associativity with right quasigroup operations. Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 53 (2019) no. 3, pp. 150-155. http://geodesic.mathdoc.fr/item/UZERU_2019_53_3_a1/

[1] J. Aczél, “On Mean Values”, Bull. Amer. Math. Soc., 54 (1948), 392–400 | DOI | MR | Zbl

[2] J. Aczél, “Remarques algebriques sur la solution donner par M. Frechet a l'equation de Kolmogoroff”, Pupl. Math. Debrecen, 4 (1955), 33–42 | MR | Zbl

[3] J. Aczél, “A Short Course on Functional Equations Based upon Recent Applications to the Social and Behavioral Sciences”, Theory and Decision Library Series B: Mathematical and Statistical Methods, D. Reidel Publishing Company, Dordrecht–Boston–Lancaster–Tokyo, 1987 | MR | Zbl

[4] J. Aczél, J. Dhombres, Functional Equations in several Variables, Cambridge University Press, New York, 1991 | MR

[5] J. Aczél, Lectures on Functional Equations and Their Applications, ed. H. Oser, Dover Publications, Mineola–New York, 2006

[6] J. Aczél, Z. Daróczy, “On measures of information and their characterizations”, Mathematics in Science and Engineering, v. 115, Academic Press, New York–San Francisco–London, 1975 | MR | Zbl

[7] J. Aczél, T. L. Saaty, “Procedures for synthesizing ratio judgements,”, Journal of Mathematical Psychology, 27:1 (1983), 93–102 | DOI | MR | Zbl

[8] Yu. M. Movsisyan, S. S. Davidov, Algebras that are nearly quasigroups, URSS, 2018 (in Russian)

[9] A. A. Albert, “Quasigroups. I”, Trans. Amer. Math. Soc., 54 (1943), 507–519 | DOI | MR | Zbl

[10] A. A. Albert, “Quasigroups. II”, Trans. Amer. Math. Soc., 55 (1944), 401–419 | DOI | MR | Zbl

[11] S. S. Davidov, A. A. Krape$\check{z}$, Yu. M. Movsisyan, “Functional Equations with Division and Regular Operations”, Asian-European Journal of Mathematics, 11:3 (2018), 1850033 | DOI | MR | Zbl

[12] A. A. Krape$\check{z}$, “Generalized Associativity on Groupoids”, Publications de l'Institut Mathematique, 28(42) (1980), 105–112 | MR | Zbl

[13] A. A. Krape$\check{z}$, “Functional Equations on Generalized Associativity, bisymmetry”, Publications de l'Institut Mathematique, 30(44) (1981), 81–87 | MR | Zbl