Generating modules efficiently over noncommutative Noetherian rings

Coutinho, S. C.

doi:10.1090/S0002-9947-1991-0986688-4

Generating modules efficiently over noncommutative Noetherian rings
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by S. C. Coutinho

Trans. Amer. Math. Soc. 323 (1991), 843-856

DOI: https://doi.org/10.1090/S0002-9947-1991-0986688-4

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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.

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