Geodesic
The description of zero divisors in monoid of semigroup varieties under wreath product
Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 8, pp. 223-231.

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It follows from the author's results published in 1999 that the wreath product of any two overcommutative semigroup varieties coincides with the variety S of all semigroups and S is the zero of the monoid MV of all semigroup varieties under the wreath product of varieties. In this paper, we give a full description of all cases under which the wreath product of two semigroup varieties equals S. 
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A. V. Tishchenko. The description of zero divisors in monoid of semigroup varieties under wreath product. Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 8, pp. 223-231. http://geodesic.mathdoc.fr/item/FPM_2006_12_8_a12/

[1] Klifford A., Preston G., Algebraicheskaya teoriya polugrupp, t. 1, 2, Mir, M., 1972

[2] Obschaya algebra, t. 2, ed. L. A. Skornyakov, Nauka, M., 1991

[3] Sapir M. V., Sukhanov E. V., “O mnogoobraziyakh periodicheskikh polugrupp”, Izv. vyssh. uchebn. zaved. Matematika, 1981, no. 4, 48–55

[4] Tischenko A. V., “Radikalnost i poluprostota spleteniya polugrupp”, Sib. mat. zhurn., 27:6 (1986), 183–195 | MR | Zbl

[5] Tischenko A. V., “Kogda monoidnoe spletenie mnogoobrazii polugrupp imeet konechnyi indeks?”, Mezhdunar. konf. po algebre pamyati A. I. Shirshova, Tezisy dokl. po logike i univers. algebram, prikl. algebre (Barnaul, avgust 1991), Novosibirsk, 1991, 144

[6] Tischenko A. V., “O razlichnykh opredeleniyakh spleteniya polugruppovykh mnogoobrazii”, Fundament. i prikl. mat., 2:1 (1996), 233–249 | MR

[7] Tischenko A. V., “Monoid polugruppovykh mnogoobrazii otnositelno spleteniya”, Uspekhi mat. nauk, 51:2 (1996), 177–178 | MR

[8] Tischenko A. V., “Spleteniya mnogoobrazii i poluarkhimedovy mnogoobraziya polugrupp”, Trudy MMO, 57 (1996), 318–338

[9] Tischenko A. V., “Uporyadochennyi monoid polugruppovykh mnogoobrazii otnositelno spleteniya”, Fundament. i prikl. matem., 5:1 (1999), 283–305 | MR | Zbl

[10] Shevrin L. N., Volkov M. V., “Tozhdestva polugrupp”, Izv. vyssh. uchebn. zaved. Matematika, 1985, no. 11, 3–47

[11] Shevrin L. N., Sukhanov E. V., “Strukturnye aspekty teorii mnogoobrazii polugrupp”, Izv. vyssh. uchebn. zaved. Matematika, 1989, no. 6, 3–39 | MR

[12] Koselev Yu. G., “Varieties preserved under wreath products”, Semigroup Forum, 12 (1976), 95–107 | DOI | MR | Zbl

[13] Skorniakov L. A., “Regularity of the wreth product of monoids”, Semigroup Forum, 18:1 (1979), 83–86 | DOI | MR

[14] Tilson B., “Categories as algebra: an essential ingredient in the theory of monoids”, J. Pure Appl. Algebra, 48:1–2 (1987), 83–198 | DOI | MR | Zbl