LINEARITY OF $n$-ARY ASSOCIATIVE ALGEBRAS

Authors

DOI:

https://doi.org/10.46991/PYSU:A/2023.57.1.009

Keywords:

regular division groupoids, n-ary groupoids, quasiendomorphisms, Schauffler theorem

Abstract

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. Schauffler like theorem will be proved for those algebras.

References

Davidov S., Krapez A., Movsisyan Yu. Functional Equations with Division and Regular Operations. Asian-Eur. J. Math. 11 (2018), 1850033. https://doi.org/10.1142/S179355711850033X

Schauffler R. Eine Anwendung Zyklischer Permutationen and Ihretheorie. Ph.D. Thesis. Marburg University (1948). https://doi.org/10.1142/12796

Schauffler R. Über die Bildung von Codewörtern. Arch. Elekt. Übertragung 10 (1956), 303-314.

Schauffler R. Die Associativität im Ganzen. Besonders bei Quasigruppen 67 (1957), 428-435.

Movsisyan Yu. Hyperidentities: Boolean and De Morgan Structures. World Scientific (2022), 560. https://doi.org/10.1142/12796

Movsisyan Yu. Introduction to the Theory of Algebras with Hyperidentities. Yerevan, YSU Press (1986) (in Russian).

Movsisyan Yu. Hyperidentities and Hypervarieties in Algebras. Yerevan, YSU Press (1990) (in Russian).

Movsisyan Yu. On a Theorem of Schauffler. Math. Notes 53 (1993), 172-179. https://doi.org/10.1007/BF01208322

Movsisyan Yu. Hyperidentities in Algebras and Varieties. Russ. Math. Surv. 53 (1998), 57-108. https://doi.org/10.1070/RM1998v053n01ABEH000009

Ushan Ya. Globally Associative Systems of $n$-ary Quasigroups (Constructions of $iA$-systems. A generalization of the Hossu-Gluskin Theorem). Publ. Inst. Math. 19 (1975), 155-165 (in Russian).

Ushan Ya., Zhizhovich M. $n$-Ary Analog of Schauffler's Theorem. Publ. Inst. Math. 19 (1975), 167-172 (in Russian).

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Published

2023-05-15

How to Cite

Harutyunyan, D. N. (2023). LINEARITY OF $n$-ARY ASSOCIATIVE ALGEBRAS. Proceedings of the YSU A: Physical and Mathematical Sciences, 57(1 (260), 9–22. https://doi.org/10.46991/PYSU:A/2023.57.1.009

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Section

Mathematics