R. Sivaramakrishnan

Certain Number-Theoretic Episodes In Algebra, Second Edition (eBook, PDF)

• Format: PDF

Produktbeschreibung

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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Produktdetails

• Verlag: Taylor & Francis
• Seitenzahl: 444
• Erscheinungstermin: 19. März 2019
• Englisch
• ISBN-13: 9781351023337
• Artikelnr.: 55857775

Autorenporträt

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 of
American 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.

Inhaltsangabe

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.