An Introduction to Commutative Algebra and Number Theory

Sukumar Das Adhikari

November 6, 2001 by Narosa
Textbook - 153 Pages
ISBN 9780849309908 - CAT# NA0990

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Features

  • Examines algebra and number theory topics at a level appropriate for a one-semester, graduate-level course
  • Assumes a basic knowledge of set theory
  • Establishes various number theoretic results throughout the sections on algebra
  • Contains a proof of the Lucas-Lehmer test
  • Includes a separate section on quadratic reciprocity that includes a complete proof of the theorem
  • Stimulates further study through the author's remarks and a thorough bibliography
  • Summary

    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.