Upper-modular and related elements of the lattice of commutative semigroup varieties

B. M. Vernikov

Upper-modular and related elements of the lattice of commutative semigroup varieties

Group Theory 2015-01-20 v2

Authors: B. M. Vernikov

Abstract

We completely determine upper-modular, codistributive and costandard elements in the lattice of all commutative semigroup varieties. In particular, we prove that the properties of being upper-modular and codistributive elements in the mentioned lattice are equivalent. Moreover, in the nil-case the properties of being elements of all three types turn out to be equivalent.

Keywords

commutative semigroup varieties lattice upper-modular elements codistributive elements costandard elements nil-case

Cite

@article{arxiv.1501.02650,
  title  = {Upper-modular and related elements of the lattice of commutative semigroup varieties},
  author = {B. M. Vernikov},
  journal= {arXiv preprint arXiv:1501.02650},
  year   = {2015}
}

Comments

16 pages, 1 figure

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