One of the first results I learned about chain conditions is that Artinian rings (satisfying d.c.c.) are automatically Noetherian (satisfying a.c.c.), and in fact a ring is Artinian if and only if it's Noetherian and has Krull dimension $0$, a very strong condition.
My question is: why are these so asymmetric? Just by looking at the chain conditions themselves you would think that they're "dual" or something, but it seems like being Artinian is such a strong condition they're not even bothered to be studied that much (by which I mean, skimming the table of contents of a few algebra books I can't even see it show up).
I'm dimly aware that this doesn't hold for modules (though this is outside the scope of what I'm currently studying) -- perhaps one way to answer my question is to explain why rings and modules differ in this respect.