ABSTRACT
Proposition 7.1. I f A is Noetherian and φ is a homomorphism o f A onto a ring B, then B is Noetherian.
Proof. This follows from (6.6), since B ~ A/a, where a — Ker (φ). m
Proposition 7.2. Let Abe a subring o f B; suppose that A is Noetherian and that B is finitely generated as an A-module. Then B is Noetherian (as a ring).
Proof. By (6.5) B is Noetherian as an .4-module, hence also as a B-module. ■
