Generating non noetherian modules constructively

Journal article, 2004

In [6], Heitmann gives a proof of a Basic Element Theorem, which has as corollaries some versions of the "Splitting-off" theorem of Serre and the Forster-Swan theorem in a non Noetherian setting. We give elementary and constructive proofs of such results. We introduce also a new notion of dimension for rings, which is only implicit in [6] and we present a generalisation of the Forster-Swan theorem, answering a question left open in [6].