Abstract. We completely determine all lower-modular elements of the lattice of all semigroup varieties. As a corollary, we show that a lower-modular element of this lattice is modular.

AMS Subject Classification (1991): 20M07, 08B15

Keyword(s): semigroup, variety, lattice of varieties, modular element, lower-modular element

Received February 24, 2010, and in final form May 6, 2010. (Registered under 15/2010.)