| Algebra: Volume II: Fields with Structure, Algebras and Advanced Topics 2008 Edition Contributor(s): Lorenz, Falko (Author), Levy, Silvio (Translator) |
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ISBN: 0387724877 ISBN-13: 9780387724874 Publisher: Springer OUR PRICE: $61.74 Product Type: Paperback - Other Formats Published: December 2007 Annotation: 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 can be recommended either as a textbook for some particular algebraic topic or as a 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., with Artin's solution of Hilbert's 17th problem and Dubois' theorem), fundamentals of the theory of quadratic forms, of valuations, local fields and modules. The book also contains some lesser known or nontraditional results; for instance, Tsen's results on solubility of systems of polynomial equations with a sufficiently large number of indeterminates. These two volumes constitute a very good, readable and comprehensive survey of classical algebra and present a valuable contribution to the literature on this subject. |
| Additional Information |
| BISAC Categories: - Mathematics | Algebra - Linear - Mathematics | Number Theory |
| Dewey: 671 |
| Series: Universitext |
| Physical Information: 0.64" H x 6.24" W x 9.19" (1.07 lbs) 340 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: This is Volume II of a two-volume introductory text in classical algebra. The text moves methodically with numerous examples and details so that readers with some basic knowledge of algebra can read it without difficulty. It is recommended either as a textbook for some particular algebraic topic or as a reference book for consultations in a selected fundamental branch of algebra. The book contains a wealth of material. Amongst the topics covered in Volume are the theory of ordered fields and Nullstellen Theorems. Known researcher Lorenz also includes the fundamentals of the theory of quadratic forms, of valuations, local fields and modules. What's more, the book contains some lesser known or nontraditional results - for instance, Tsen's results on the solubility of systems of polynomial equations with a sufficiently large number of indeterminates. |