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Algebraic number theory is a branch of number theory in which the concept of a number is expanded to the algebraic numbers which are roots of polynomials with rational coefficients. An algebraic number field is any finite (and therefore algebraic) field extension of the rational numbers. These domains contain elements analogous to the integers, the socalled algebraic integers. In this setting, the familiar features of the integers (e.g. unique factorization) need not hold. The virtue of the machinery employed — Galois theory, group cohomology, class field theory, group representations and Lfunctions — is that it allows one to recover that order partly for this new class of numbers. Algebraic number theory, Introductory , Şaban Alaca, Kenneth S. Williams Algebraic number theory, Problems in , Maruti Ram Murty, Jody Esmonde Classical theory of algebraic numbers, Paulo Ribenboim See also * List of algebraic number theory topics * Algebraic number fields Retrieved from "http://en.wikipedia.org/"

