Certain Number-Theoretic Episodes In Algebra, 2nd Edition

Certain Number-Theoretic Episodes In Algebra, 2nd Edition
PDF, ePUB
  • eBook:
    Certain Number-Theoretic Episodes In Algebra, 2nd Edition
  • Author:
    R Sivaramakrishnan
  • Edition:
    2 edition
  • Categories:
  • Data:
    March 26, 2019
  • ISBN:
    1138495786
  • ISBN-13:
    9781138495784
  • Language:
    English
  • Pages:
    444 pages
  • Format:
    PDF, ePUB

Book Description
The book attempts to point out the interconnections between number theory and algebra with a view to making a student understand certain basic concepts in the two areas forming the subject-matter of the book.

Content

Section I - ELEMENTS OF THE THEORY OF NUMBERS. . 1
1. From Euclid to Lucas: Elementary Theorems Revisited
2. Solutions of Congruences, Primitive Roots
3. The Chinese Remainder Theorem
4. Mobius Inversion
5. Quadratic Residues (mod r) (r > 1)
6. Decomposition of a Number as a Sum of Two or Four Squares
7. Dirichlet Algebra of Arithmetical Functions
8. Modular Arithmetical Functions
9. A Generalization of Ramanujan Sums
10. Ramanujan Expansions of Multiplicative Arithmetic Functions

Section II - SELECTED TOPICS IN ALGEBRA
11. On the Uniqueness of a Group of Order r (r > 1)
12. Quadratic Reciprocity in a Finite Group
13. Commutative Rings with Unity
14. Noetherian and Artinian Rings

Section III - GLIMPSES OF THE THEORY OF ALGEBRAIC NUMBERS
15. Dedekind Domains
16. Algebraic Number Fields

Section IV - SOME ADDITIONAL TOPICS
17. Vaidyanathaswamy’s Class-Division of Integers Modulo r
18. Burnside’s Lemma and a Few of Its Applications
19. On Cyclic Codes of Length n over Fq
20. An Analogue of the Goldbach Problem

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