Generating modules efficiently over noncommutative Noetherian rings

Abstract

The Forster-Swan Theorem gives an upper bound on the number of generators of a module over a commutative ring in terms of local data. Stafford showed that this theorem could be generalized to arbitrary right and left noetherian rings. In this paper a similar result is proved for right noetherian rings with finite Krull dimension. A new dimension function—the basic dimension—is the main tool used in the proof of this result.