A question for the lattice theorists:
is it known if the quasi-variety of balanced
lattices with 0 is actually a variety?
[Using ^ for meet and v for join, a lattice
with 0 is said to be balanced if the following
quasi-identity holds:
(x ^ y) v (x v y) ^ z = 0 implies (y v z) ^ x = 0.
A lattice is strongly balanced if every nonempty
interval is balanced. Strongly balanced lattices
are also characterized by a quasi-identity.]
Sorry if this is well-known. I know virtually
nothing about the various generalizations of
modularity.
MK