Geodesic
Upper-modular elements of the lattice of semigroup varieties.~II
Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 7, pp. 43-51

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A semigroup variety is called a variety of degree $\le2$ if all its nilsemigroups are semigroups with zero multiplication, and a variety of degree $>2$ otherwise. We completely determine all semigroup varieties of degree $>2$ that are upper-modular elements of the lattice of all semigroup varieties and find quite a strong necessary condition for semigroup varieties of degree $\le2$ to have the same property. 
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     author = {B. M. Vernikov},
     title = {Upper-modular elements of the lattice of semigroup {varieties.~II}},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {43--51},
     publisher = {mathdoc},
     volume = {14},
     number = {7},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2008_14_7_a4/}
}
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B. M. Vernikov. Upper-modular elements of the lattice of semigroup varieties.~II. Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 7, pp. 43-51. http://geodesic.mathdoc.fr/item/FPM_2008_14_7_a4/