Geodesic
The multiplicative group of a~field and hyperidentities
Izvestiya. Mathematics , Tome 35 (1990) no. 2, pp. 377-391.

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The multiplicative group of a field is characterized. By means of a hyperidentity of distributivity, the groups that can be distinguished as the multiplicative group of a field by the hyperidentity of idempotency are characterized. Bibliography: 21 titles. 
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Yu. M. Movsisyan. The multiplicative group of a~field and hyperidentities. Izvestiya. Mathematics , Tome 35 (1990) no. 2, pp. 377-391. http://geodesic.mathdoc.fr/item/IM2_1990_35_2_a4/

[1] Fuks L., Beskonechnye abelevy gruppy, t. 2, Mir, M, 1977

[2] Dicker R. M., “A set of independent axioms for a field and a condition for a group tobe the multiplicative group of a field”, Proc. London Math. Soc., 18 (1968), 114–124 | DOI | MR | Zbl

[3] Cohn P. M., “On the embedding of rings in skew fields”, Proc. London Math. Soc., 11 (1961), 511–530 | DOI | MR | Zbl

[4] May W., “Multiplicative groups of fields”, Proc. London Math. Soc., 24 (1972), 295–306 | DOI | MR | Zbl

[5] Brauer R., “On a theorem of H. Cartan”, Bull. Amer. Math. Soc., 55 (1949), 619–620 | DOI | MR | Zbl

[6] Hua L. K., “Some properties of sfields”, Proc. Nat. Acad. Sci., 35 (1949), 533–537 | DOI | MR | Zbl

[7] Schenkman E., “Some remarks on the multiplicative group of a sfield”, Proc. Amer. Math. Soc., 9:2 (1958), 231–235 | DOI | MR | Zbl

[8] Schenkman E., Scott W. R., “A generalization of the Cartan–Brauer–Hua theorem”, Proc. Amer. Math. Soc., 11:3 (1960), 396–398 | DOI | MR | Zbl

[9] Khuzurbazar M. Sh., “K teorii multiplikativnykh grupp tel”, Dokl. AN SSSR, 137:1 (1961), 42–44 | Zbl

[10] Herstein I. N., “A remark on division rings with involution”, Indian J. Pure and Appl. Math., 9:3 (1978), 267–269 | MR | Zbl

[11] Ershov Yu. L., Lavrov I. A., Taimanov A. D., Taitslin M. A., “Elementarnye teorii”, UMN, 20:4 (1965), 37–108 | MR | Zbl

[12] Kogalovskii S. R., “O multiplikativnykh polugruppakh kolets”, Dokl. AN SSSR, 140:5 (1961), 1005–1007 | MR | Zbl

[13] Sabbagh G., “How not to characterize the multiplicative groups of fields”, J. London Math. Soc., 1 (1969), 369–370 | DOI | MR | Zbl

[14] Maltsev A. I., Algebraicheskie sistemy, Nauka, M., 1970 | MR

[15] Skornyakov L. A., “Stokhasticheskaya algebra”, Izv. vuzov. Matematika, 1985, no. 7, 3–11 | MR | Zbl

[16] Taylor W., “Hyperidentities and hypervarieties”, Aequationes Mathematicae, 23 (1981), 30–49 | DOI | MR | Zbl

[17] Bergman G. M., “Hyperidentities of groups and semigroups”, Aequationes Mathematicae, 23 (1981), 50–65 | DOI | MR

[18] Penner P., “Hyperidentities of lattices and semilattices”, Algebra Universalis, 13 (1981), 307–314 | DOI | MR | Zbl

[19] Movsisyan Yu. M., Vvedenie v teoriyu algebr so sverkhtozhdestvami, EGU, Erevan, 1986 | MR

[20] Bruck R. H., A survey of binary systems, Springer-Verlag, Berlin, Heidelberg, Göttingen, 1958 | MR | Zbl

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