Geodesic
Codistributive elements of the lattice of semigroup varieties
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2011), pp. 13-21

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We prove that if a semigroup variety is a codistributive element of the lattice SEM of all semigroup varieties then it either coincides with the variety of all semigroups or is a variety of semigroups with completely regular square. We completely classify strongly permutative varieties that are codistributive elements of SEM. We prove that a semigroup variety is a costandard element of the lattice SEM if and only if it is a neutral element of this lattice. In view of results obtained earlier, this gives a complete description of costandard elements of the lattice SEM.
Keywords: semigroup, variety, lattice, codistributive element, costandard element
Mots-clés : neutral element. 
@article{IVM_2011_7_a1,
     author = {B. M. Vernikov},
     title = {Codistributive elements of the lattice of semigroup varieties},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {13--21},
     publisher = {mathdoc},
     number = {7},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2011_7_a1/}
}
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B. M. Vernikov. Codistributive elements of the lattice of semigroup varieties. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2011), pp. 13-21. http://geodesic.mathdoc.fr/item/IVM_2011_7_a1/