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Generating non-Noetherian modules constructively. (English) Zbl 1059.13006

This paper contains constructive proofs of a Basic Element theorem and versions of the “splitting-off” theorems of Serre and Forster-Swan in the non-Noetherian setting. As a tool the authors introduce a new notion of dimension for rings.

MSC:

13C15 Dimension theory, depth, related commutative rings (catenary, etc.)
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