Abstract. We find a multiplication on the lattice of existence varieties of locally inverse semigroups which extends the classical multiplication of group varieties and the recently found multiplication of inverse semigroup varieties. As a special case we get an associative multiplication on the lattice of varieties of completely simple semigroups.

AMS Subject Classification (1991): 20M07, 08B20

Received April 11, 1996. (Registered under 5775/2009.)