Varieties ofl-groups are finitely based

We deal with varieties of lattice-ordered groups {ie149-1} defined by the identity xⁿ, yⁿ]=e. The structure of subdirectly indecomposable l-groups in the variety {ie149-2} is studied, and we establish that l-varieties satisfying the identity xⁿ, yⁿ]=e and generated by a finitely generated l-group are finitely based. It is shown that l-varieties {ie149-3} with finite axiomatic rank {ie149-4} also have finite bases of identities. Translated fromAlgebra i Logika, Vol. 35, No. 3, pp. 268–287, May–June, 1996.