Algebraic Number Theory (CRC Press Series on Discrete Mathematics and Its Application)

From its history as an elegant but abstract area of mathematics, algebraic number theory now takes its place as a useful and accessible study with important real-world practicality. Unique among algebraic number theory texts, this important work offers a wealth of applications to cryptography, including factoring, primality-testing, and public-key cryptosystems. A follow-up to Dr. Mollin's popular "Fundamental Number Theory with Applications", Algebraic Number Theory provides a global approach to the subject that selectively avoids local theory. Instead it carefully leads the reader through each topic from the level of the algebraic integer, to the arithmetic of number fields, to ideal theory, and closes with reciprocity laws. In each chapter the author includes a section on a cryptographic application of the ideas presented, effectively demonstrating the pragmatic side of theory. In this way, Algebraic Number Theory provides a comprehensible yet thorough treatment of the material. Written with the prerequisite background provided in appendices so that anyone with a knowledge can work through the book, this one-of-a-kind text brings the subject matter to life with historical background and real-world practicality.

Provides a global approach to the subject, leading readers through algebraic numbers, the arithmetic of field numbers, ideal theory, ideal decomposition in extension fields, and reciprocity laws. Each chapter includes a section on a cryptographic application of ideas presented, demonstrating the pragmatic side of theory. Engages readers by offering a historical perspective through the lives of mathematicians who played key roles in developing algebraic number theory. Includes chapter exercises, and background appendices. For a course for senior undergraduate and beginning graduate students. Annotation c. by Book News, Inc., Portland, OR (booknews@booknews.com)

A follow-up to Dr. Mollin's Fundamental Number Theory with Applications, Algebraic Number Theory provides an accessible approach to the subject by relegating local theory to an appendix. Leading the student from the level of elements, to the field, and then the ideal levels, the author presents a comprehensible yet thorough text that includes the recent application of algebraic number theory to secure cryptographic schemes.

Includes bibliographical references (p. 459-463) and index.

Algebraic Numbers.- Arithmetic of Number Fields.- Ideals.- Diophantine Equations.- Reciprocity Laws.- Galois Theory.- Applications.- Appendices.