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Maximal orders by Reiner, Irving is a nonfiction available to read on EtoBox.
What is Maximal orders about?
This is a reissue of a classic text, which includes the author's own corrections and provides a very accessible, self contained introduction to the classical theory of orders and maximal orders over a Dedekind ring. It starts wtih a long chapter that provides the algebraic prerequisites for this theory, covering basic material on Dedekind domains, localizations and completions as well as semisimple rings and separable algebras. This is followed by an introduction to the basic tools in studying orders, such as reduced norms and traces, discriminants, and localization of orders. The theory of maximal orders is then developed in the local case, first in a complete setting, and then over any discrete valuation ring. This paves the way to a chapter on the ideal theory in global maximal orders with detailed expositions on ideal classes, the jordan-Zassenhaus Theorum and genera. This is followed by a chapter on Brauer groups and crossed product algebras, where Hasse's theory of cyclic algebras over local fields is presented in a clear and self-contained fashion. Assuming a couple of facts from class field theory, the book goes on to present the theory of simple algebras over global fields
Who reads Maximal orders?
It is typically read by self-directed learners exploring a subject in depth.
Common subject areas: history, science, philosophy, social sciences.
- Author
- Reiner, Irving
- Publisher
- London ; Academic Press, 1975.
- Published
- 1975
- Language
- EN
- ISBN
- 9780125866507
- Category
- nonfiction
- Subjects
- Mathematics, Stem
Other editions & translations
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