Linearity of $n$-ary associative algebras
Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 57 (2023) no. 1, pp. 9-22.

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In this paper $n$-ary regular division associative algebras are discussed. It is shown that every operation in $n$-ary regular division associative algebra will be endo-linearly represented over the same binary group. Schaufler like theorem will be proved for those algebras.
Keywords: $\forall\exists(\forall)$-identities, regular division groupoids, $n$-ary groupoids, quasiendomorphisms, Schaufler theorem.
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D. N. Harutyunyan. Linearity   of  $n$-ary  associative  algebras. Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 57 (2023) no. 1, pp. 9-22. http://geodesic.mathdoc.fr/item/UZERU_2023_57_1_a1/

[1] 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

[2] R. Schauffler, Eine Anwendung Zyklischer Permutationen and Ihretheorie, Ph.D. Thesis, Marburg University, 1948 | DOI

[3] R. Schauffler, “Über die Bilding von Codewörtern”, Arch. Electr. Übertragung, 10:7 (1957), 303–314 | MR

[4] R. Schauffler, “Die Assoziativität im Ganzen besonders bei Quasigruppen”, Math. Zeitschr., 67:5 (1957), 428–435 | DOI | MR | Zbl

[5] Yu. M. Movsisyan, Hyperidentities: Boolean and De Morgan Structures, World Scientific, 1986, 560 pp. | DOI | MR

[6] Yu. M. Movsisyan, Introduction of The Theory of Algebras with Hyperidentities, Yerevan State University Press, Yerevan, 1986 (Russian) | MR

[7] Yu. M. Movsisyan, Hyperidentities and Hypervarieties in Algebras, Yerevan State University Press, 1990 (in Russian) | MR

[8] Yu. M. Movsisyan, On a Theorem of Schauffler, 53:2 (1993), 172–179 | DOI | MR | Zbl

[9] Yu. M. Movsisyan, “Hyperidentities in Algebras and Varieties”, Russian Math. Surveys, 53 (1998), 57–108 | DOI | MR | Zbl

[10] Ya. Ushan, “Globally Associative Systems of $n$-ary Quasigroups (Constructions of $iA$-systems. A generalization of the Hossu–Gluskin Theorem”, Publ. Inst. Math., 19:33 (1975), 155–165 (in Russian) | MR

[11] Ya. Ushan, M. Zhizhovich, “$n$-Ary Analog of Schauffler's Theorem”, Publ. Inst. Math., 19:33 (1975), 167–172 (in Russian) | MR