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The product of finitely based varieties of lattice-ordered groups

Authors:	M V Litvinova

Abstract:	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 varieties $(\mathcal{L}_\mathfrak{n} \cap \mathfrak{A}^2 ) \cdot V$ and $\mathfrak{N}_\mathfrak{s} \cdot V$ are finitely based; here $(\mathcal{L}_\mathfrak{n} \cap \mathfrak{A}^2 ) \cdot V$ is a variety of lattice-ordered groups defined by identities x ⁿ,y ⁿ] =e and x,y] z, x ₁,y ₁] z ₁] =e; $\mathfrak{N}_\mathfrak{s}$ is a variety of lattice-ordered nilpotent groups of class s, defined by an identity x ₁,x ₂,...,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.

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