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Zbl 1024.16008
Reiner, I.
Maximal orders. Reprint of the 1975 original. (English)
[B] London Mathematical Society Monographs. New Series. 28. Oxford: Oxford University Press. xiv, 395 p. \sterling 70.00 (2003). ISBN 0-19-852673-3/hbk

28 years after its first appearence, Irving Reiner's book ``Maximal orders'' has remained to be a standard reference to ``non-commutative arithmetics''. Apart from the classical applications already mentioned in the book, there are some areas of currently active research, like non-commutative algebraic geometry or non-Abelian Iwasawa theory, where the theory of maximal orders has become an important requisite.\par Not only for maximal orders, but also for general orders over a Dedekind domain, Reiner's book provides an excellent introduction for students and serves as an indispensible reference for researchers. For a summary of contents we refer to the review Zbl 0305.16001 of the original.
[Wolfgang Rump (Stuttgart)]

MSC 2000:: *16H05 Orders and arithmetic, separable associative algebras
16-02 Research monographs (assoc. rings and algebras)
16U30 Divisibility, noncommutative UFDs
16K20 Finite-dimensional division rings
16P50 Localization and associative Noetherian rings
11R52 Quaternion and other division algebras: arithmetic, zeta functions
16G30 Representations of orders, etc. over commutative rings
11S45 Algebras and orders, and their zeta functions
14F22 Brauer groups of schemes
01A75 Collected or selected works

Keywords: maximal orders; Dedekind domains; separable algebras; reduced norms; traces; localizations; completions; discrete valuation rings; Brauer groups; crossed products; simple algebras; hereditary orders

Citations: Zbl 0305.16001

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