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Certain number-theoretic episodes in algebra / R. Sivaramakrishnan.

By: Sivaramakrishnan, R, 1936- [author.].
Material type: materialTypeLabelBookSeries: Chapman & Hall/CRC Pure and Applied Mathematics.Publisher: Boca Raton : Chapman & Hall/CRC, 2019Edition: Second edition.Description: 1 online resource : illustrations (black and white).Content type: text | still image Media type: computer Carrier type: online resourceISBN: 9781351023320; 1351023322; 9781351023337; 1351023330; 9781351023313; 1351023314; 9781351023344; 1351023349.Subject(s): Algebraic number theory | Number theoryDDC classification: 512.74 Online resources: Taylor & Francis | OCLC metadata license agreement
Contents:
Section A -- ELEMENTS OF THE THEORY OF NUMBERS. From Euclid to Lucas: Elementary theorems revisited. Solutions of Congruences, Primitive Roots. The Chinese Remainder Theorem. M·obius inversion. Quadratic Residues. Decomposition of a number as a sum of two or four squares. Dirichlet Algebra of Arithmetical Functions. Modular arithmetical functions. A generalization of Ramanujan sums. Ramanujan expansions of multiplicative arithmetic functions. Section B -- SELECTED TOPICS IN ALGEBRA. On the uniqueness of a group of order r (r > 1). Quadratic Reciprocity in a finite group. Commutative rings with unity. Noetherian and Artinian rings. Section C -- GLIMPSES OF THE THEORY OF ALGEBRAIC NUMBERS. Dedekind domains. Algebraic number fields. Section D -- SOME ADDITIONAL TOPICS. Vaidyanathaswamy's class-division of integers modulo r. Burnside's lemma and a few of its applications. On cyclic codes of length n over Fq. An Analogue of the Goldbach problem. Appendix A. Appendix B. Appendix C. Index.
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Previous edition: 2007.

Section A -- ELEMENTS OF THE THEORY OF NUMBERS. From Euclid to Lucas: Elementary theorems revisited. Solutions of Congruences, Primitive Roots. The Chinese Remainder Theorem. M·obius inversion. Quadratic Residues. Decomposition of a number as a sum of two or four squares. Dirichlet Algebra of Arithmetical Functions. Modular arithmetical functions. A generalization of Ramanujan sums. Ramanujan expansions of multiplicative arithmetic functions. Section B -- SELECTED TOPICS IN ALGEBRA. On the uniqueness of a group of order r (r > 1). Quadratic Reciprocity in a finite group. Commutative rings with unity. Noetherian and Artinian rings. Section C -- GLIMPSES OF THE THEORY OF ALGEBRAIC NUMBERS. Dedekind domains. Algebraic number fields. Section D -- SOME ADDITIONAL TOPICS. Vaidyanathaswamy's class-division of integers modulo r. Burnside's lemma and a few of its applications. On cyclic codes of length n over Fq. An Analogue of the Goldbach problem. Appendix A. Appendix B. Appendix C. Index.

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