Certain Number-Theoretic Episodes In Algebra, Second Edition

2. Auflage 2019
ISBN: 978-1-138-49578-4
Verlag: Chapman and Hall/CRC

Buch, Englisch, 444 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 831 g

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.

Zielgruppe

Professional and Professional Practice & Development

Autoren/Hrsg.

Sivaramakrishnan, R.

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Zahlentheorie

Inhaltsverzeichnis

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.

Über Autor(innen)

Sivaramakrishnan Ramakrishna Ayyar has served a few educational institutions in Kerala as a math-teacher. In particular, he has served the university of Calicut, Kerala-673635 during the years 1977-1996.
A monograph entitled: ‘Classical Theory of Arithmetic Functions’ (Marcel Dekker (1989)) was published during his visitorship (1987-88) at the University of Kansas, Lawrence, KS66045, U.S.A. He has also visited Mangalore University (1996-1997), Mangalagangotri, Mangalore-574199. He holds an Emeritus membership ofAmerican Mathematical Society, since 2008. His e-mail address is: [e-mail].
The first edition of this book was published in the year 2006 (Chapman & Hall/CRC (Tayor & Francis Group)) when he could receive a Government of India Grant under ‘Utilization of Services of Retired Scientists’ (USERS) scheme to work at the University of Calicut during the two-year period April, 2000–March, 2002.