Non-Commutative Valuation Rings and Semi-Hereditary Orders

ISBN-13: 9789048148530 / Angielski / Miękka / 2010 / 192 str.

H. Marubayashi; Haruo Miyamoto; Akira Ueda

Opis

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 Prufer 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.

Spis treści

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.