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Certain Number-theoretic Episodes in Algebra - 9780824758950

Un libro in lingua di R. Sivaramakrishnan edito da Taylor & Francis, 2006

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Sivaramakrishnan (mathematics, U. of Calicut) finds it true that it is desirable to learn algebra via number theory and to learn number theory via algebra. He starts by covering the classical theorems, then describes the integral domain of rational integers, Euclidean domains, rings of polynomials and former power series, the Chinese remainder theorem and the evaluation of a number of solutions of a linear congruence with side conditions, reciprocity laws, and finite groups. He analyzes the relevance of algebraic structures to number theory in such topics as ordered fields, fields with valuation and other algebraic structures, the role of the Möbius function and of generating functions, semigroups and certain convolution algebras. He then moves to algebraic number theory with Noetherian domains, Dedekind domains and algebraic number fields, closing with a section on interconnections that examines rings of arithmetic functions, and analogies of the Goldbach problem. Annotation ©2006 Book News, Inc., Portland, OR (booknews.com)

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