Certain number-theoretic episodes in algebra/ R Sivaramakrishnan

Includes bibliographical references and index

Section I - ELEMENTS OF THE THEORY OF NUMBERS -- 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 -- 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 -- 15. 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 -- Appendix A -- Appendix B -- Appendix C. Index.

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.