Geodesic
Distributive and neutral elements of the lattice of commutative semigroup varieties
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2011), pp. 67-79.

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We completely determine commutative semigroup varieties that are distributive, standard or neutral elements of the lattice of all commutative semigroup varieties. In particular, it turns out that the properties of being a distributive element and of being a standard element in this lattice are equivalent.
Keywords: semigroup, variety, lattice, distributive element, standard element.
Mots-clés : neutral element 
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V. Yu. Shaprynskii. Distributive and neutral elements of the lattice of commutative semigroup varieties. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2011), pp. 67-79. http://geodesic.mathdoc.fr/item/IVM_2011_7_a7/

[1] Shevrin L. N., Vernikov B. M., Volkov M. V., “Reshetki mnogoobrazii polugrupp”, Izv. vuzov. Matem., 2009, no. 3, 3–36 | MR | Zbl

[2] Grettser G., Obschaya teoriya reshetok, Mir, M., 1982 | MR

[3] Burris S., Nelson E., “Embedding the dual of $\Pi_m$ in the lattice of equational classes of commutative semigroups”, Proc. Amer. Math. Soc., 30:1 (1971), 37–39 | MR | Zbl

[4] Perkins P., “Bases for equational theories of semigroups”, J. Algebra, 11:2 (1969), 298–314 | DOI | MR | Zbl

[5] Kisielewicz A., “Varieties of commutative semigroups”, Trans. Amer. Math. Soc., 342:1 (1994), 275–306 | DOI | MR | Zbl

[6] Ježek J., “The lattice of equational theories. Part I: modular elements”, Czechosl. Math. J., 31:1 (1981), 127–152 | MR

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

[8] Vernikov B. M., “Upper-modular elements of the lattice of semigroup varieties”, Algebra Universalis, 59:3–4 (2008), 405–428 | DOI | MR | Zbl

[9] Sapir M. V., Sukhanov E. V., “O mnogoobraziyakh periodicheskikh polugrupp”, Izv. vuzov. Matem., 1981, no. 4, 48–55 | MR | Zbl

[10] Vernikov B. M., Volkov M. V., “Commuting fully invariant congruences on free semigroups”, Contrib. General Algebra, 12 (2000), 391–417 | MR | Zbl

[11] Korjakov I. O., “A scetch of the lattice of commutative nilpotent semigroup varieties”, Semigroup Forum, 24:4 (1982), 285–317 | DOI | MR | Zbl

[12] Volkov M. V., “Mnogoobraziya polugrupp s modulyarnoi reshetkoi podmnogoobrazii”, Izv. vuzov. Matem., 1989, no. 6, 51–60 | MR

[13] Tischenko A. V., “Zamechanie o polugruppovykh mnogoobraziyakh konechnogo indeksa”, Izv. vuzov. Matem., 1990, no. 7, 79–83 | MR | Zbl