The product of finitely based varieties of lattice-ordered groups

The question as to whether a product of two finitely based varieties of lattice-ordered groups is finitely based is considered. It is proved that varietiesandare finitely based; hereis a variety of lattice-ordered groups defined by identities [xⁿ,yⁿ] =e and [[x,y] z, [x₁,y₁] z₁] =e;is a variety of lattice-ordered nilpotent groups of class s, defined by an identity [x₁,x₂,...,x_(s+1)] =e; V is an arbitrary finitely based variety of lattice-ordered groups.Translated fromAlgebra i Logika, Vol. 33, No. 3, pp. 255–263, May–June, 1994.Supported by the Russian Foundation for Fundamental Research, grant No. 93-011-1524.