Geodesic
On the rank of coefficientless equations in four unknowns in a free semigroup
Sbornik. Mathematics, Tome 29 (1976) no. 2, pp. 257-280 Cet article a éte moissonné depuis la source Math-Net.Ru

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A survey of definitions of the rank of a coefficientless equation in a free semigroup is given. An algorithm is constructed which for every equation in four unknowns in a free semigroup discerns whether the rank of the equation is three or less than three. Bibliography: 5 titles. 
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G. S. Makanin. On the rank of coefficientless equations in four unknowns in a free semigroup. Sbornik. Mathematics, Tome 29 (1976) no. 2, pp. 257-280. http://geodesic.mathdoc.fr/item/SM_1976_29_2_a9/

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

[2] K. I. Appel, F. M. Djorup, “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

[3] Yu. I. Khmelevskii, Uravneniya v svobodnoi polugruppe, Trudy Matem. in-ta im. V. A. Steklova, CVII, 1971

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

[5] G. S. Makanin, “Preobrazovaniya beskoeffitsientnykh uravnenii v svobodnoi polugruppe”, Vsesoyuznyi algebr. simpozium, Gomel, 1975, 227–228