Geodesic
Recognition of the rank of equations in a~free semigroup
Izvestiya. Mathematics , Tome 14 (1980) no. 3, pp. 499-545.

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An algorithm is constructed which calculates the rank of any coefficient-free equation in a free semigroup (coefficient-free word equation). Bibliography: 10 titles. 
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G. S. Makanin. Recognition of the rank of equations in a~free semigroup. Izvestiya. Mathematics , Tome 14 (1980) no. 3, pp. 499-545. http://geodesic.mathdoc.fr/item/IM2_1980_14_3_a1/

[1] Makanin G. S., “O range beskoeffitsientnykh uravnenii v svobodnoi polugruppe”, Matem. sb., 100(142):2(6) (1976), 285–311 | MR | Zbl

[2] Skordew D., Sendow B., “Ob uravneniyakh v slovakh”, Z. Math. Logic und Grundl. Math., 7:4 (1961), 289–297 | Zbl

[3] Appel K. I., Djorup F. M., “On the equation $z_1^nz_2^n\dots z_k^n=y^n$ in a free semigroup”, Trans. Amer. Math. Soc., 134 (1968), 461–470 | DOI | MR | Zbl

[4] Khmelevskii Yu. I., Uravneniya v svobodnoi polugruppe, Tr. Matem in-ta im. V. A. Steklova AN SSSR, CVII, 1971

[5] Lentin A., Equations dans les monoides libres, Gauthie-Villar, Paris, 1972 | MR | Zbl

[6] Khmelevskii Yu. I., “Beskoeffitsientnye sistemy s 4 neizvestnymi v svobodnoi polugruppe”, Z. Math. Logic und Grundl. Math., 23 (1977), 59–90 | DOI

[7] Makanin G. S., “Problema raspoznavaniya maksimalnogo ranga uravnenii v svobodnoi polugruppe”, 14-ya Vsesoyuzn. algebraicheskaya konferentsiya, Novosibirsk, 1977

[8] Makanin G. S., “Problema razreshimosti uravnenii v svobodnoi polugruppe”, Matem. sb., 103(145):2(6) (1977), 147–236 | MR | Zbl

[9] Adyan S. I., Problema Bernsaida i tozhdestva v gruppakh, Nauka, M, 1975 | MR | Zbl

[10] Ershov Yu. L., Lavrov I. A., Taimanov A. D. i Taitslin M. A., “Elementarnye teorii”, Uspekhi matem. nauk, XX:4(124) (1965), 37–108