Maximal orders. Reprint of the 1975 original.

*(English)*Zbl 1024.16008London 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.

Reviewer: Wolfgang Rump (Stuttgart)

##### MSC:

16H05 | Separable associative algebras |

16-02 | Research monographs (associative 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, lattices, algebras over commutative rings |

11S45 | Algebras and orders, and their zeta functions |

14F22 | Brauer groups of schemes |

01A75 | Collected or selected works |