Abstract:
A semigroup variety is called a variety of degree$\le2$ 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 $\le2$ to have the same property.
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