Geodesic
Decidability of the positive theory of a free countably generated semigroup
Sbornik. Mathematics, Tome 44 (1983) no. 1, pp. 109-116 Cet article a éte moissonné depuis la source Math-Net.Ru

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A decision procedure for the positive theory of a free countably generated semigroup is constructed, with a bound on the number of steps, obtained by modifying an algorithm from work of G. S. Makanin (see Matem. Sb. (N.S.), 103(145) (1977), 147–236). Bibliography: 7 titles. 
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Yu. M. Vazhenin; B. V. Rozenblat. Decidability of the positive theory of a free countably generated semigroup. Sbornik. Mathematics, Tome 44 (1983) no. 1, pp. 109-116. http://geodesic.mathdoc.fr/item/SM_1983_44_1_a5/

[1] Ershov Yu. L., Lavrov I. A., Taimanov A. D., Taitslin M. A., “Elementarnye teorii”, UMN, XX:4 (1965), 37–108

[2] Durnev V. G., “O pozitivnykh formulakh na svobodnykh polugruppakh”, Sib. matem. zh., 15:5 (1974), 1131–1137 | MR | Zbl

[3] Makaniya G. S., “Problema razreshimosti uravnenii v svobodnoi polugruppe”, Matem. sb., 103 (145) (1977), 147–236

[4] Durnev V. G., “O pozitivnoi teorii svobodnoi polugruppy”, Voprosy teorii grupp i polugrupp, Tulsk. gos. ped. in-t, Tula, 1972, 122–172 | MR

[5] Peryazev Ya. A., Fridman E. Ya., “O pozitivnykh teoriyakh svobodnykh sistem mnogoobrazii algebr”, Tez. dokl. V Vses. konf. po matem. logike, Novosibirsk, 1979, 122

[6] Durnev V. G., “O pozitivnykh formulakh na gruppakh”, Uch. zap. matem. kaf. Tulskogo gos. ped. in-ta, geometriya i algebra, 1970, no. 2, 215–241 | MR

[7] Maltsev A. Ya., Algebraicheskie sistemy, Nauka, M., 1970 | MR