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Non-Commutative Valuation Rings and Semi-Hereditary Orders : K-Monographs in Mathematics - Hidetoshi Marubayashi

Non-Commutative Valuation Rings and Semi-Hereditary Orders

K-Monographs in Mathematics


Published: 31st May 1997
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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 PrA1/4fer 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.

Semi-Hereditary and Prufer Ordersp. 1
Dubrovin Valuation Ringsp. 21
Semi-Local Bezout Ordersp. 79
The Applications and Examplesp. 109
Semi-perfect rings and serial ringsp. 174
Coherent ringsp. 175
Azumaya algebrasp. 177
The lifting idempotentsp. 178
Wedderburn's Theoremp. 181
Referencesp. 183
Index of Notationp. 188
Indexp. 190
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792345626
ISBN-10: 0792345622
Series: K-Monographs in Mathematics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 192
Published: 31st May 1997
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 23.5 x 15.5  x 1.91
Weight (kg): 1.03