Other metaproperties

[rschwiebert]

Suggestions by dyunov in #38

• [x] By Kerr's examples, right ACC annihilator passes neither to polynomial nor to matrix rings (see Lam II p328–329), and neither does right Goldie.

For the following three see Lam II ex14–16 p18.

• [x] IBN pass to matrices, polynomial and power series rings

• [x] stable finiteness pass to matrices, polynomial and power series rings

• [ ] (the "rank condition" — is it included in DaRT?) pass to matrices, polynomial and power series rings

• [x] IC also passes to power series rings (5.4 in Khurana — Lam), corners (5.6), but not to polynomial rings (5.10) and is not Morita invariant (5.9)(3).

• [x] Jacobson (Hilbert) doesn't pass to power series rings: $\mathbb Q \subset \mathbb Q[[x]]$.

• [x] Jacobson (Hilbert) doesn't pass to localizations: $\mathbb Z\subset \mathbb Z_{(2)}$.

• [x] Noetherian passes to polynomials and power series.

[rschwiebert]

Later we should add counterexamples to secure the cases that IC is not preserved in polynomial rings or matrix rings.

[rschwiebert]

Going to defer on rank condition right now.