Certain Number-Theoretic Episodes In Algebra: 1st Edition (Paperback) book cover

Certain Number-Theoretic Episodes In Algebra

1st Edition

By Sivaramakrishnan R, R Sivaramakrishnan

Chapman and Hall/CRC

632 pages

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Description

Many basic ideas of algebra and number theory intertwine, making it ideal to explore both at the same time. Certain Number-Theoretic Episodes in Algebra focuses on some important aspects of interconnections between number theory and commutative algebra. Using a pedagogical approach, the author presents the conceptual foundations of commutative algebra arising from number theory. Self-contained, the book examines situations where explicit algebraic analogues of theorems of number theory are available.

Coverage is divided into four parts, beginning with elements of number theory and algebra such as theorems of Euler, Fermat, and Lagrange, Euclidean domains, and finite groups. In the second part, the book details ordered fields, fields with valuation, and other algebraic structures. This is followed by a review of fundamentals of algebraic number theory in the third part. The final part explores links with ring theory, finite dimensional algebras, and the Goldbach problem.

Table of Contents

Elements of Number Theory and Algebra. The Relevance of Algebraic Structures to Number Theory. A Glimpse of Algebraic Number Theory. Some More Interconnections.

About the Authors

R, Sivaramakrishnan; Sivaramakrishnan, R

Subject Categories

BISAC Subject Codes/Headings:
MAT000000
MATHEMATICS / General
MAT002000
MATHEMATICS / Algebra / General
MAT022000
MATHEMATICS / Number Theory