Equations satisfied by finite modular lattices I found this very interesting paper by Freese, The Variety of Modular Lattices is Not Generated by its Finite Members, which shows that finite modular lattices satisfy an identity that is not satisfied by arbitrary modular lattices.  Is more known about this?  For example, is a complete list of identities satisfied by finite modular lattices but not general modular lattices known?
 A: Until someone shows up who is less than a decade removed from studying the material involved, I will offer my unverified opinion.
A key property involved here is residual finiteness,  which arises in the paper of Ralph Freese  mentioned above.  He shows that the lattice L he builds has the property that for any M with a homomorphism onto L, M is not residually finite.  This implies M is not a subdirect product of finite modular lattices, so L is not in the variety generated by finite modular lattices.
In the 90's, Ralph McKenzie proved a slough of undecidability results for general algebras, in particular regarding finite axiomatizability and residual smallness. (Yes, I was there.) The upshot is that I feel (but do not guarantee) there will not be a computable way to list identities not satisfied by general modular lattices if it will depend on constructing residually small (residually less than some cardinal) modular lattices.  Note that I do not know if residual smallness is decidable if we restrict to just lattice varieties, so the feeling above needs more backing to it.
Gerhard "Waiting For Some Professional Commentary" Paseman, 2017.08.28.
