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Maximal orders. Reprint of the 1975 original. (English) Zbl 1024.16008
London Mathematical Society Monographs. New Series. 28. Oxford: Oxford University Press. xiv, 395 p. £70.00 (2003).

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.

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.

MSC:
16H05Separable associative algebras
16-02Research monographs (associative rings and algebras)
16U30Divisibility, noncommutative UFDs
16K20Finite-dimensional division rings
16P50Localization and associative Noetherian rings
11R52Quaternion and other division algebras: arithmetic, zeta functions
16G30Representations of orders, lattices, algebras over commutative rings
11S45Algebras and orders, and their zeta functions
14F22Brauer groups of schemes
01A75Collected or selected works