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Hereditary Noetherian prime rings, 3: Infinitely generated projective modules

✍ Scribed by Lawrence S. Levy; J. Chris Robson

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 153 KB
Volume: 225
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1999.8123

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✦ Synopsis

We describe the structure of infinitely generated projective modules over hereditary Noetherian prime rings. The isomorphism invariants are uniform dimension and ranks at maximal ideals. Infinitely generated projective modules need not be free. However, every uncountably generated projective module is the direct sum of a finitely generated module and free modules over specific finite overrings of the given ring in its Goldie quotient ring.

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This is the first of three papers that aim to bring the known theory of projective modules over a hereditary Noetherian prime ring R up to roughly the same level as the well-known commutative case, where R is a Dedekind domain. This first paper lays the foundations by introducing the notion of an in