Certain number-theoretic episodes in algebra.0824758951 Certain number-theoretic episodes in algebra. Sivaramakrishnan, R. Chapman & Hall/CRC 2007 632 pages $139.95 Hardcover Pure and applied mathematics; 286 QA247 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 con·gru·ence n. 1. a. Agreement, harmony, conformity, or correspondence. b. An instance of this: "What an extraordinary congruence of genius and era" with side conditions, reciprocity laws, and finite groups. He analyzes the relevance of algebraic structures In universal algebra, a branch of pure mathematics, an algebraic structure consists of a set closed under one or more operations, satisfying a number of axioms, including none. Abstract algebra is primarily the study of algebraic structures and their properties. to number theory in such topics as ordered fields, fields with valuation and other algebraic structures, the role of the Mobius function and of generating functions, semigroups and certain convolution convolution /con·vo·lu·tion/ (-loo´shun) a tortuous irregularity or elevation caused by the infolding of a structure upon itself. algebras. He then moves to algebraic number theory Algebraic number theory is a branch of number theory in which the concept of a number is expanded to the algebraic numbers which are mathematic roots of polynomials with rational number coefficients. with Noetherian domains, Dedekind domains and algebraic number fields In mathematics, an algebraic number field (or simply number field) F is a finite, (and hence algebraic) field extension of the field of rational numbers Q. , closing with a section on interconnections that examines rings of arithmetic functions, and analogies of the Goldbach problem. ([c]20062005 Book News, Inc., Portland, OR) |
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