書誌事項

Separable algebras

Timothy J. Ford

(Graduate studies in mathematics, v. 183)

American Mathematical Society, c2017

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注記

Includes bibliographical references (p. 621-629) and index

内容説明・目次

内容説明

This book presents a comprehensive introduction to the theory of separable algebras over commutative rings. After a thorough introduction to the general theory, the fundamental roles played by separable algebras are explored. For example, Azumaya algebras, the henselization of local rings, and Galois theory are rigorously introduced and treated. Interwoven throughout these applications is the important notion of etale algebras. Essential connections are drawn between the theory of separable algebras and Morita theory, the theory of faithfully flat descent, cohomology, derivations, differentials, reflexive lattices, maximal orders, and class groups. The text is accessible to graduate students who have finished a first course in algebra, and it includes necessary foundational material, useful exercises, and many nontrivial examples.

目次

Background material on rings and modules Modules over commutative rings The Wedderburn-Artin theorem Separable algebras, definition and first properties Background material on homological algebra The divisor class group Azumaya algebras, I Derivations, differentials and separability Etale algebras Henselization and splitting rings Azumaya algebras, II Galois extensions of commutative rings Crossed products and Galois cohomology Further topics Acronyms Glossary of notation Bibliography Index.

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