Abstract. It is well known that exactly two subvarieties of the variety of lattices cover the variety of distributive lattices. In a generalization of lattices, the weakly associative lattices, three more covering varieties are known. In this paper we consider a further generalization, weak lattices. We get this variety by omitting all identities keeping only the eight absorption laws. We shall prove that in this variety the variety of distributive lattices is covered by infinitely many subvarieties.

AMS Subject Classification (1991): 06A20

Keyword(s): weak lattice, weakly associative lattice, absorption law, variety

Received December 14, 2007, and in final form March 20, 2009. (Registered under 6419/2009.)