In my adventures I've finally come by a copy of Examples of Commutative Rings by Hutchins, and almost immediately read something that surprised me.
On page 10, a regular ring is defined as Noetherian ring whose every localization at a maximal ideal is a regular local ring.
Up until now, I thought the standard definition was that it was rather a Noetherian ring whose every localization at a prime ideal is a regular local ring.
I'm not handy with commutative algebra... is the definition using maximal ideals a thing? Or are they equivalent and I just haven't run across the theorem?
Am I apparently going to have to re-interpret everything he says about regular rings?