Field Theory

Graduate Texts in Mathematics #158

by Steven Roman

About the Field Theory Intended for graduate courses or for independent study, this book presents the basic theory of fields. The first part begins with a discussion of polynomials over a ring, the division algorithm, irreducibility, field extensions, and embeddings. The second part is devoted to Galois theory. The third part of the book treats the theory of binomials. The book concludes with a chapter on families of binomials-the Kummer theory. This new edition has been completely rewritten in order to improve the pedagogy and to make the text more accessible to graduate students. The exercises have also been improved and a new chapter on ordered fields has been included. Contents Part I-Basic Linear Algebra Chapter 1: Vector Spaces Chapter 2: Linear Transformations Chapter 3: The Isomorphism Theorems Chapter 4: Modules Basic Properties Chapter 5: Modules Free and Noetherian Modules Chapter 6: Modules over a Principal Ideal Domain Chapter 7: The Structure of a Linear Operator Chapter 8: Eigenvalues and Eigenvectors Chapter 9: Real and Complex Inner Product Spaces Chapter 10: Structure Theory for Normal Operators, Part II-Topics, Chapter 11: Metric Vector The Theory of Bilinear Forms, Chapter 12: Metric Spaces, Chapter 13: Hilbert Spaces, Chapter 14: Tensor Products, Chapter 15: Positive Solutions to Linear Convexity and Separation Chapter 16: Affine Geometry, Chapter 17: Operator QR and Singular Value, Chapter 18: The Umbral Calculus References Index,

Genres: Mathematics, Science, Theory, Algebra

Hardcover

Published January 1, 2006