noetherian ring
ring whose ideals satisfy the ascending chain condition
excellent ring
a Noetherian universally catenary ring that is J-2 and Grothendieck
catenary ring
commutative ring admitting a good dimension function, i.e. that relative dimension between two prime ideals is well defined, in the sense that any maximal strictly increasing chain of prime ideals between the two has the same finite length
Dedekind domain
Ring with unique factorization for ideals (mathematics)