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.

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