Certain Number-Theoretic Episodes In Algebra
Publisher: CRC Press
Published: 2006
Place of publication: Hoboken
Language: eng
Format: [electronic resource]
Number of pages: 660
ISBN-13: 9781420015065
Subjects: Algebraic number theory
Description: There are many intersections between the fields of algebra and number theory, and in certain cases there exist explicit algebraic analogues of theorems from number theory. Presenting the tools needed to explore these linkages, this reference explains the conceptual foundations of commutative algebra arising from number theory.
Notes: Description based on print version record.
Table of contents: title: Front Cover; ACKNOWLEDGEMENT; PREFACE; ABOUT THE AUTHOR; CONTENTS; CHAPTER 1. Theorems of Euler, Fermat and Lagrange; CHAPTER 2. The integral domain of rational integers; CHAPTER 3. Euclidean domains; CHAPTER 4. Rings of polynomials and formal power series; CHAPTER 5. The Chinese Remainder Theorem and the evaluation of number of solutions of a linear congruence with side conditions; CHAPTER 6. Reciprocity laws; CHAPTER 7. Finite groups; CHAPTER 8. Ordered fields, fields with valuation and order algebraic structures; CHAPTER 9. The role of the Mobius function- Abstract Mobius inversion.; title: CHAPTER 10. The role of generating functionsCHAPTER 11. Semigroups and certain convolution algebras; CHAPTER 12. Noetherian and Dedekind domains; CHAPTER 13. Algebraic number fields; CHAPTER 14. Rings of arithmetic functions; CHAPTER 15. Analogues of the Goldbach problem; CHAPTER 16. An epilogue: More interconnections; True/False statements : Answer key; Index of some selected structure theorems/results; Index of symbols an.