Ring-shaped stars around black holes

While listening to this lady talk about black holes and how they can only gobble up material at a certain speed, producing a material backup within the accretion disk, she also mentioned that if there is enough material in the disk, fusion can occur within it. At that point, even though gravity is trying to thin the disk out, fusion puts internal pressure on the disk and it expands - the very same struggle that defines stars.

It then occurred to me - aren't they then just tiny ring-shaped stars in a state of perpetual orbital decay? Black holes gobble up space-time, too, right? So that means the ring is also in a state of perpetual expansion, but the rate at which it expands is equal to the rate that space-time is falling into the black hole. Now, I'm no astrophysicist, but I'm just gonna assume ring-stars are real until a real astrophysicist tells me they're not. I'll call them Annulustars! No, no, no... Torustars! No... Brentars!

So be it! Brentars are born!