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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{FPM_2008_14_7_a4,
     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/}
}
TY  - JOUR
AU  - B. M. Vernikov
TI  - Upper-modular elements of the lattice of semigroup varieties.~II
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2008
SP  - 43
EP  - 51
VL  - 14
IS  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2008_14_7_a4/
LA  - ru
ID  - FPM_2008_14_7_a4
ER  - 
%0 Journal Article
%A B. M. Vernikov
%T Upper-modular elements of the lattice of semigroup varieties.~II
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2008
%P 43-51
%V 14
%N 7
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2008_14_7_a4/
%G ru
%F FPM_2008_14_7_a4
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/

[1] Vernikov B. M., Volkov M. V., “Reshëtki nilpotentnykh mnogoobrazii polugrupp”, Algebraicheskie sistemy i ikh mnogoobraziya, Ural. gos. un-t, Sverdlovsk, 1988, 53–65 | MR

[2] Volkov M. V., “Mnogoobraziya polugrupp s modulyarnoi reshëtkoi podmnogoobrazii”, Dokl. RAN, 326:3 (1992), 409–413 | MR | Zbl

[3] Volkov M. V., “Mnogoobraziya polugrupp s modulyarnoi reshëtkoi podmnogoobrazii. III”, Izv. vyssh. uchebn. zaved. Matematika, 1992, no. 8, 21–29 | MR | Zbl

[4] Golubov E. A., Sapir M. V., “Finitno approksimiruemye mnogoobraziya polugrupp”, Izv. vyssh. uchebn. zaved. Matematika, 1982, no. 11, 21–29 | MR | Zbl

[5] Rasin V. V., “Mnogoobraziya ortodoksalnykh kliffordovykh polugrupp”, Izv. vyssh. uchebn. zaved. Matematika, 1982, no. 11, 82–85 | MR | Zbl

[6] Shevrin L. N., Vernikov B. M., Volkov M. V., “Reshëtki mnogoobrazii polugrupp”, Izv. vyssh. uchebn. zaved. Matematika, 2009, no. 3, 3–36 | MR | Zbl

[7] Gerhard J. A., “Semigroups with an idempotent power. II. The lattice of equational subclasses of $[(xy)^2=xy]$”, Semigroup Forum, 14:4 (1977), 375–388 | DOI | MR | Zbl

[8] Ježek J., McKenzie R. N., “Definability in the lattice of equational theories of semigroups”, Semigroup Forum, 46:2 (1993), 199–245 | MR

[9] Polák L., “On varieties of completely regular semigroups. I”, Semigroup Forum, 32:1 (1985), 97–123 | DOI | MR | Zbl

[10] Vernikov B. M., “Lower-modular elements of the lattice of semigroup varieties”, Semigroup Forum, 75:3 (2007), 554–566 | DOI | MR

[11] Vernikov B. M., “On modular elements of the lattice of semigroup varieties”, Comment. Math. Univ. Carolin., 48:4 (2007), 595–606 | MR | Zbl

[12] Vernikov B. M., “Lower-modular elements of the lattice of semigroup varieties. II”, Acta Sci. Math. (Szeged), 74 (2008), 539–556 | MR | Zbl

[13] Vernikov B. M., “Upper-modular elements of the lattice of semigroup varieties”, Algebra Universalis (to appear) | MR

[14] Vernikov B. M., Volkov M. V., “Modular elements of the lattice of semigroup varieties. II”, Contrib. General Algebra, 17 (2006), 173–190 | MR | Zbl

[15] Volkov M. V., “Commutative semigroup varieties with distributive subvariety lattices”, Contrib. General Algebra, 7 (1991), 351–359 | MR | Zbl

[16] Volkov M. V., “Modular elements of the lattice of semigroup varieties”, Contrib. General Algebra, 16 (2005), 275–288 | MR | Zbl