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Hereditary Noetherian Prime Rings 2. Finitely Generated Projective Modules

โœ Scribed by Lawrence S Levy; J.Chris Robson

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
219 KB
Volume
218
Category
Article
ISSN
0021-8693

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โœฆ Synopsis

Let R be a hereditary Noetherian prime ring. We determine a full set of invariants for the isomorphism class of any finitely generated projective R-module of uniform dimension at least 2. In particular we prove that P โŠ• X โˆผ = Q โŠ• X implies P โˆผ = Q whenever P has uniform dimension at least 2. Among the applications of these results are necessary and sufficient conditions for the existence of a bound to the number of generators needed for right ideals of R.

๐Ÿ“œ SIMILAR VOLUMES

Hereditary Noetherian prime rings, 3: In
Hereditary Noetherian prime rings, 3: Infinitely generated projective modules
โœ Lawrence S. Levy; J. Chris Robson ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 153 KB

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

Hereditary Noetherian Prime Rings 1. Int
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โœ Lawrence S Levy; J.Chris Robson ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 185 KB

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