Non-Commutative Valuation Rings and Semi-Hereditary Orders by Hidetoshi MarubayashiNon-Commutative Valuation Rings and Semi-Hereditary Orders by Hidetoshi Marubayashi

Non-Commutative Valuation Rings and Semi-Hereditary Orders

byHidetoshi Marubayashi, Haruo Miyamoto, Akira Ueda

Paperback | December 7, 2010

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This is the first self-contained summary of non-Noetherian orders in a simple Artinian ring, a subject in which much progress has been made in the last decade. The contents of the book are mainly Dubrovin valuation rings and semi-hereditary orders, including Prüfer and semi-local Bezout orders, which are considered, in a sense, as global theories of Dubrovin valuation rings. These are then developed further, and applied to give some examples such as Dubrovin valuation rings in crossed product algebras, semi-hereditary maximal order in certain matrix rings, and the idealizers of semi-hereditary orders and Henselization of Bezout orders. Audience: This volume will be of interest to researchers and graduate students whose work involves non-commutative ring theory and module theory.
Title:Non-Commutative Valuation Rings and Semi-Hereditary OrdersFormat:PaperbackDimensions:200 pages, 10.98 × 8.27 × 0 inPublished:December 7, 2010Publisher:Springer NetherlandsLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9048148537

ISBN - 13:9789048148530

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Table of Contents

Preface. I. Semi-Hereditary and Prüfer Orders. II. Dubrovin Valuation Rings. III. Semi-Local Bezout Orders. IV. The Applications and Examples. Appendix: A1. Semi-Perfect Rings and Serial Rings. A2. Coherent Rings. A3. Azumaya Algebras. A4. The Lifting Idempotents. A5. Wedderburn's Theorem. References. Index of Notation. Index.