From Math Reviews: This is Volume II of a two-volume introductory text in classical algebra. The text moves carefully with many details so that readers with some basic knowledge of algebra can read it without difficulty. The book canbe recommended either as a textbook for some particular algebraic topic or asa reference book for consultations in a selected fundamental branch of algebra. The book contains a wealth of material. Amongst the topics covered in Volume II the reader can find: the theory of ordered fields (e.g., with reformulation of the fundamental theorem of algebra in terms of ordered fields, with Sylvester's theorem on the number of real roots), Nullstellen-theorems (e.g., withArtin's solution of Hilbert's 17th problem and Dubois' theorem), fundamentalsof the theory of quadratic forms, of valuations, local fields and modules. Nicely written comprehensive survey of classical algebra INDICE: Foreword.- Ordered fields and real fields.- Hilbert's seventeenth problem and the real nullstellensatz.- Orders and quadratic forms.- Absolute values on fields.- Residue class degree and ramification index.- Local fields.- Witt vectors.- The tsen rank of a field.- Fundamentals of modules.- Wedderburn theory.- Crossed products.- The brauer group of a local field.- Local class field theory.- Semisimple representations of finite groups.- The schur group of a field.- Appendix: problems and remarks.- Index.
- ISBN: 978-0-387-72487-4
- Editorial: Springer
- Encuadernacion: Rústica
- Páginas: 345
- Fecha Publicación: 01/01/2008
- Nº Volúmenes: 1
- Idioma: Inglés
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