Certain Number-Theoretic Episodes In Algebra (Chapman & Hall/CRC Pure and Applied Mathematics) by R Sivaramakrishnan
Certain Number-Theoretic Episodes In Algebra (Chapman & Hall/CRC Pure and Applied Mathematics)
Author: R Sivaramakrishnan
Title: Certain Number-Theoretic Episodes In Algebra (Chapman & Hall/CRC Pure and Applied Mathematics)
ISBN10: 0824758951
ISBN13: 978-0824758950
Format: .PDF .EPUB .FB2
Pages:
Publisher: Chapman and Hall/CRC; 1 edition (September 22, 2006)
Language: English
Size pdf: 1642 kb
Size epub: 1541 kb
Rating: 3.6 ✪
Votes: 414
Category: Science & Math
Subcategory: Mathematics
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.