FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2008, VOLUME 14, NUMBER 7, PAGES 43-51

**Upper-modular elements of the lattice of semigroup varieties. II**

B. M. Vernikov

Abstract

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A semigroup variety is called a *variety of
degree* $$£ 2 if all its
nilsemigroups are semigroups with zero multiplication, and
a *variety of degree* $>\; 2$ otherwise.
We completely determine all semigroup varieties of
degree $>\; 2$ that are upper-modular elements of the lattice
of all semigroup varieties and find quite a strong necessary
condition for semigroup varieties of degree $$£
2 to have the same property.

Location: http://mech.math.msu.su/~fpm/eng/k08/k087/k08705h.htm

Last modified: June 25, 2009