On some quasi-identities in finite quasigroups
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2005), pp. 19-32.

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In this article we consider some quasi-identities in quasigroups, in particular, quasi-identities connected with parastrophic orthogonality of a quasigroup. We also research some quasi-identities in quasigroups (in loops) with one parameter δ (δ-quasi-identities) which arose by the study of detecting coding systems such as check character systems in [6] (see also [5, 7]), establish equivalence of such quasi-identities, connection of some of them with orthogonality of quasigroups and give a number of examples of finite quasigroups with such δ-quasi-identities.
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G. Belyavskaya; A. Diordiev. On some quasi-identities in finite quasigroups. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2005), pp. 19-32. https://geodesic-test.mathdoc.fr/item/BASM_2005_3_a2/

[1] Artamonov A., Salii V. N., Skornyakov L. A., General algebra, Vol. 2, Moscow, 1991 (in Russian)

[2] Belousov V. D., “On properties of binary operations”, Uchenie zapiski of Bel'skogo pedinstituta, 1960, no. 5, 9–28 (in Russian)

[3] Belousov V. D., Foundations of the quasigroup and loop theory, Nauka, Moscow, 1967 (in Russian) | MR

[4] Belousov V. D., “Systems of orthogonal operations”, Mat. sbornik, 77(119):1 (1968), 38–58 (in Russian) | MR | Zbl

[5] Belyavskaya G. B., “On check character systems over quasigroups and loops”, Algebra and discrete mathematics, 2003, no. 2, 1–13 | MR | Zbl

[6] Belyavskaya G. B., Izbash V. I., Mullen G. L., “Check character systems using quasigroups, I”, Designs, Codes and Cryptography, 37 (2005), 215–227 | DOI | MR | Zbl

[7] Belyavskaya G. B., Izbash V. I., Shcherbacov V. A., “Check character systems over quasigroups and loops”, Quasigroups and related systems, 10 (2003), 1–28 | MR | Zbl

[8] Damm M., Pruefziffersysteme ueber Quasigruppen, Diplomarbeit Universitaet Marburg, Maerz, 1998

[9] Deneš J., Keedwell A. D., Latin squares and their applications, Academiai Kiado, Budapest, 1974 | MR

[10] Ecker A., Poch G., “Check character systems”, Computing, 1986, no. 37(4), 277–301 | DOI | MR | Zbl

[11] Gorbunov V. A., Algebraic theory of quasi-varieties, Novosibirsk, 1998 (in Russian)

[12] Mal'cev A. I., Algebraic systems, Nauka, Moscow, 1970 (in Russian) | MR

[13] Mann H. B., “On orthogonal latin squares”, Bull. Amer. Math. Soc., 50 (1944), 249–257 | DOI | MR | Zbl

[14] Mullen G. L., Shcherbacov V. A., “On orthogonality of binary operations and squares”, Buletinul A. Ş. M., Matematica, 2005, no. 2(48), 3–42 | MR

[15] Sade A., “Produit direct-singular di quasigroups orthogonaux et anti-abelians”, Ann. Soc. Sci., Bruxelles, Ser. I, 74 (1960), 91–99 | MR | Zbl

[16] Schulz R.-H., “On check digit systems using anti-symmetric mappings”, Number, Information and Complexity, eds. J. Althofer. et al., Kluwer Acad. Publ., Boston, 2000, 295–310 | MR | Zbl

[17] Verhoeff I., Error Detecting Decimal Codes, Math. Center Tracts, 29, Amsterdam, 1969 | MR | Zbl