Non-Commutative Valuation Rings and Semi-Hereditary Orders
By: by Hidetoshi Marubayashi, Haruo Miyamoto, Akira Ueda
Contributors: Miyamoto, Haruo; Ueda, Akira
Series: K-Monographs in Mathematics -- 3; K-Monographs in Mathematics -- 3
Publisher: Springer Netherlands
Published: 1997
Place of publication: Dordrecht
Language: eng
Format: [electronic resource] /
Number of pages: 192
ISBN-13: 9789048148530; 9789401724364
Subjects: Mathematics; Field theory (Physics); Algebra
Description: 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.
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