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Home > Mathematics and Science books > Mathematics > Groups and group theory > An Introduction to Commutative Algebra and Number Theory
An Introduction to Commutative Algebra and Number Theory

An Introduction to Commutative Algebra and Number Theory


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About the Book

An Introduction to Commutative Algebra and Number Theory is an elementary introduction to these subjects. Beginning with a concise review of groups, rings and fields, the author presents topics in algebra from a distinctly number-theoretic perspective and sprinkles number theory results throughout his presentation. The topics in algebra include polynomial rings, UFD, PID, and Euclidean domains; and field extensions, modules, and Dedekind domains. In the section on number theory, in addition to covering elementary congruence results, the laws of quadratic reciprocity and basics of algebraic number fields, this book gives glimpses into some deeper aspects of the subject. These include Warning's and Chevally's theorems in the finite field sections, and many results of additive number theory, such as the derivation of LaGrange's four-square theorem from Minkowski's result in the geometry of numbers. With addition of remarks and comments and with references in the bibliography, the author stimulates readers to explore the subject beyond the scope of this book.

Table of Contents:
Preface. Notations and Terminologies. Preliminaries: Groups, Rings and Fields. The Integers. Polynomial Rings. Exercise Set A. Rings and Fields Revisited. Factorization. Gauss Lemma and Eisenstein Criterion. Field Extension. Quadratic Reciprocity Law. Exercise Set B. Modules. Gaussian Integers and the Ring Z [v-5] Algebraic Number Fields-I. Exercise Set C. Dedekind domains. Algebraic Number Fields-II. Exercise Set D. Quadratic Fields. Solutions to Selected Exercises. Appendix: Lucas-Lehmer Test. Bibliography. Index.


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Product Details
  • ISBN-13: 9780849309908
  • Publisher: Narosa Publishing House
  • Publisher Imprint: Narosa Publishing House
  • Height: 190 mm
  • No of Pages: 153
  • Returnable: N
  • Width: 127 mm
  • ISBN-10: 0849309905
  • Publisher Date: 06 Nov 2001
  • Binding: Hardback
  • Language: English
  • No of Pages: 153
  • Weight: 358 gr


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