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Certain Number-Theoretic Episodes In Algebra, Second Edition de R Sivaramakrishnan

Certain Number-Theoretic Episodes In Algebra, Second Edition

Autor R Sivaramakrishnan
en Limba Engleză Hardback – 26 mar 2019
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.
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Specificații

ISBN-13: 9781138495784
ISBN-10: 1138495786
Pagini: 444
Ilustrații: 3 Tables, black and white; 47 Illustrations, black and white
Dimensiuni: 156 x 234 x 25 mm
Greutate: 0.75 kg
Ediția:Nouă
Editura: CRC Press
Colecția Chapman and Hall/CRC

Public țintă

Professional and Professional Practice & Development

Cuprins

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.

Descriere

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.