Beschreibung:
Prof. Dr. Falko Lorenz lehrt an der Universität Münster Mathematik und ist auswärtiges Mitglied der Akademie gemeinnütziger Wissenschaften zu Erfurt.
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.
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.
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. 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.
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.
