Geodesic
Linear representation of binary Abelian algebras
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2005), pp. 58-63.

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In the present paper binary Аbelian algebras are studied by bringing them to known algebraic structures such as monoids. We have found conditions when binary Аbelian algebra has a linear representation, i.e. every operation of Аbelian algebra can be expressed by operation and endomorphisms of commutative monoid. 
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S. S. Davidov. Linear representation of binary Abelian algebras. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2005), pp. 58-63. http://geodesic.mathdoc.fr/item/UZERU_2005_3_a4/

[1] Yu. M. Movsisyan, “Sverkhtozhdestva v algebrakh i mnogoobraziyakh”, UMN, 53 (1998), 61–114 | DOI | MR | Zbl

[2] J. Jezek, T. Kerka, Medial groupoids, Praha, 1983 | MR

[3] A. G. Kurosh, Obschaya algebra, Nauka, M., 1974 | MR

[4] A. V. Romanovska, J. D. H. Smith, Modes, World Scientific, Singapore, 2002

[5] J.D.H. Smith, “Entropy, character theory and centrality of finite quasigroups”, Math. Proc. Cambridge Philos. Soc., 108 (1990), 435–443 | DOI | MR