## On the lattice of approximable $$\ell$$-varieties.(Russian)Zbl 0551.06017

An $$\ell$$-variety satisfying $$(x\wedge y^{-1} x^{-1}y) \vee e=e$$ is called o-approximable. The author shows that the lattice $$L_ o$$ of all o-approximable $$\ell$$-varieties has not the covering property (namely, he constructs a variety $$V\in L_ o$$ which is not the greatest element of $$L_ o$$ and has no cover in $$L_ o)$$. Further, he proves that $$L_ o$$ is not a Brouwer lattice and finds the base ranks (minimal number of generators of $$\ell$$-groups generating the given variety) for $$\ell$$- varieties given by $$(x\wedge y^{-1} x^{-1}y)\vee e=e$$ and by $$| x| | y| \wedge | y|^ 2| x|^ 2=| x| | y|$$; they are 2 in both cases. Finally, he constructs an $$\ell$$-variety having no independent equational base.
Reviewer: V.Novák

### MSC:

 06F15 Ordered groups 08B15 Lattices of varieties 06B20 Varieties of lattices
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