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. 
@article{FPM_2006_12_8_a12,
     author = {A. V. Tishchenko},
     title = {The description of zero divisors in monoid of semigroup varieties under wreath product},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {223--231},
     publisher = {mathdoc},
     volume = {12},
     number = {8},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2006_12_8_a12/}
}
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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/