Compounds with aluminum and nitrogen atoms directly bonded to each other as part of an aromatic ring? Just hours ago, I asked a question about whether aromatic organoaluminum compounds with aluminum and carbon bonded together as part of an aromatic ring would be stable in water. The answer seemed to be that "it wouldn't even work at all since aluminum and carbon have relatively poor pi-overlap, and even then the resulting compound would still end up complexing with nitrogen- or oxygen-based protic solvents due to the high affinity for nitrogen and oxygen of aluminum", implying that aluminum-nitrogen bonds are reasonably stable, at least when they're alone by themselves.
My questions are- do aluminum and nitrogen have sufficient p-orbital overlap to be directly bonded to each other as part of an aromatic ring, and, if they do, how stable are they to different kinds of solvents (protic, aprotic, polar, non-polar etc), and is there any specific compound reported in the literature that is water-stable and in which there is a direct aluminum-nitrogen bond as part of an aromatic ring? (Note that these need not be organoaluminum compounds- that is to say, the aluminum atom in question need not be bonded to any carbon atoms)
Again no.  The aluminum-nitrogen bond is much stronger as a sigma bond than as a pi bond.

Borazine, with boron rather than aluminum in the six-membered ring, is known as an aromatic ring and even called "inorganic benzene".  Like its benzene counterpart, the borazine ring can be fused to give polymeric structures ultimately leading to hexagonal boron nitride.  But with aluminum nitride, where pi overlap is weaker and the bonding more polar, such a layered phase is not known, this nitride most commonly having a wurtzite structure.  In effect, the Al-N pi bonds are broken up by cross-linking with other nitrogen atoms even where the pi bonded structure is ostensibly aromatic.

Take a cue from this answer.  You are on firmest ground with aromaticity when the elements involved are a subset of boron, carbon, nitrogen, oxygen, sulfur.