Geodesic
Special elements of certain types in the lattice of epigroup varieties
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 3, pp. 244-250 Cet article a éte moissonné depuis la source Math-Net.Ru

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Lower-modular, codistributive and costandard elements of the lattice of all epigroup varieties are studied. Lower-modular and costandard elements are completely classified, and codistributive elements are described within a wide class of epigroup varieties that includes all commutative varieties. In particular, we verify that, in the lattice of all epigroup varieties, an element is costandard if and only if it is neutral and an element is modular whenever it is lower-modular.
Keywords: epigroup, variety, lattice, lower-modular element, codistributive element, costandard element.
Mots-clés : neutral element 
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D. V. Skokov. Special elements of certain types in the lattice of epigroup varieties. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 3, pp. 244-250. http://geodesic.mathdoc.fr/item/TIMM_2016_22_3_a24/

[1] Vernikov B.M., “Kodistributivnye elementy reshetki mnogoobrazii polugrupp”, Izv. vuzov. Matematika, 2011, no. 7, 13–21 | MR | Zbl

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

[3] Skokov D.V., “Distributivnye elementy reshetki mnogoobrazii epigrupp”, Sib. elektron. mat. izv., 12 (2015), 723–731 | Zbl

[4] Shaprynskii V.Yu., “Distributivnye i neitralnye elementy reshetki kommutativnykh mnogoobrazii polugrupp”, Izv. vuzov. Matematika, 2011, no. 7, 67–79 | MR | Zbl

[5] Shevrin L.N., “K teorii epigrupp. I”, Mat. sb., 185:8 (1994), 129-160 | MR | Zbl

[6] Gratzer G., Lattice Theory: Foundation, Springer Basel AG, Birkhauser, 2011, 614 pp. | MR

[7] Gusev S.V., Vernikov B.M., “Endomorphisms of the lattice of epigroup varieties”, 22 pp., arXiv: http://arxiv.org/abs/1404.0478v3

[8] Shaprynski V.Yu., “Modular and lower-modular elements of lattices of semigroup varieties”, Semigroup Forum, 85:1 (2012), 97–110 | DOI | MR | Zbl

[9] Shaprynski V.Yu., Skokov D.V., Vernikov B.M., “Special elements of the lattice of epigroup varieties”, Algebra Universalis, 76:1 (2016), 1–30 | DOI | MR | Zbl

[10] Shaprynski V.Yu., Vernikov B.M., “Lower-modular elements of the lattice of semigroup varieties.III”, Acta Sci. Math. (Szeged), 76:3–4 (2010), 371–382 | MR | Zbl