> is it known if the quasi-variety of balanced
> lattices with 0 is actually a variety?

It is not a variety. If you add a new zero element to any lattice L with
zero it becomes balanced, and L is a quotient of this new balanced
lattice. Thus, the variety generated by balanced lattices is the variety
of all lattices with zero, not all of which are balanced.

--
Keith A. Kearnes Email: kearnes@...
Department of Mathematics WWW: http://spot.colorado.edu/~kearnes
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