A Laskerian ring is a ring in which every ideal has a primary decomposition. The Lasker-Noether theorem states that every commutative Noetherian ring is a Laskerian ring (as an easy consequence of the ascending chain condition).
And I've found the statement that there are non-Noetherian Laskerian rings, but I can't find an example. Any ideas?
Edit. As the tag already suggested, I'm particularly interested in a commutative Laskerian non-Noetherian ring, but noncommutative examples are also welcome. It never hurts to know more counterexamples.