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.
Oxide Thin Films and Nanostructures is an interdisciplinary approach to introduce readers to the field of oxide nano-materials, that is oxides of nano-meter size and dimensions. Emphasis is put to differentiate these nanoscale oxide objects from their solid bulk oxide parents and present their properties in a pedagogic way.
Magnetic resonance imaging (MRI) has become the leading cross-sectional imaging method in clinical practice. Continuous technical improvements have significantly broadened the scope of applications. At present, MR imaging is not only the most important diagnostic technique in neuroradiology and musculoskeletal radiology, but has also become an invaluable diagnostic tool for abdominal, pelvic, cardiac, breast and vascular imaging. This book offers practical guidelines for performing efficient and cost-effective MRI examinations in daily practice. The underlying idea is that, by adopting a practical protocol-based approach, the work-flow in a MRI unit can be streamlined and optimized. For the second edition, all chapters have been thoroughly reviewed, and new techniques and figures were included. This book will help beginners to advance their starting point in implementing the protocols and will aid more experienced users in updating their knowledge.
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.
This translation of the 1987 German edition is an introduction into the classical parts of algebra with a focus on fields and Galois theory. It discusses nonstandard topics, such as the transcendence of pi, and new concepts are defined in the framework of the development of carefully selected problems. It includes an appendix with exercises and notes on the previous parts of the book, and brief historical comments are scattered throughout.
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