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Hereditary Noetherian Prime Rings 1. Integrality and Simple Modules

✍ Scribed by Lawrence S Levy; J.Chris Robson

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 185 KB
Volume: 218
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1999.7884

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✦ Synopsis

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 integral extension S of R in the Goldie quotient ring of R, and elucidating the relationship between integrality and the R-module structure of simple S-modules.

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Hereditary Noetherian Prime Rings 2. Finitely Generated Projective Modules

✍ Lawrence S Levy; J.Chris Robson 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 219 KB

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 ⊕ X ∼ = Q ⊕ X implies P ∼ = Q whenever P has uniform dimension at least 2. Among t

Hereditary Noetherian prime rings, 3: In

Hereditary Noetherian prime rings, 3: Infinitely generated projective modules

✍ Lawrence S. Levy; J. Chris Robson 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 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