Algebra with Galois theory.9780821841297 Algebra with Galois theory. Artin, Emil. American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards to mathematicians. 2007 126 pages $29.00 Paperback Courant Cou`rant´ a. 1. (Her.) Represented as running; - said of a beast borne in a coat of arms. n. 1. A piece of music in triple time; also, a lively dance; a coranto. 2. lecture notes; 15 QA214 Artin's approach begins with his analysis of groups, including the concept of a group itself and the phenomena of subgroups. He describes rings and fields, including linear equations in a field and vector spaces, polynomials over a field, factorization fac·tor·ize tr.v. fac·tor·ized, fac·tor·iz·ing, fac·tor·iz·es Mathematics To factor. fac into primes, ideals and the greatest common divisor (mathematics) greatest common divisor - (GCD) A function that returns the largest positive integer that both arguments are integer multiples of. See also Euclid's Algorithm. Compare: lowest common multiple. , solution of the general equation of nth degree, residual classes, extension fields, and isomorphisms. He explains Galois theory, including such topics as splitting fields and their automorphisms, the characteristics of a field, derivation of a polynomial polynomial, mathematical expression which is a finite sum, each term being a constant times a product of one or more variables raised to powers. With only one variable the general form of a polynomial is a0xn+a (multiple roots), the degree of an extension field, group characters, fundamental theorems and finite fields, then moves to polynomials with integral coefficients, including irreducibility and primitive roots of unity, and the theory of equations, including ruler and compass constructions, and the theorems of Steinitz and Abel. This classic 1947 treatment, formerly titled Modern Higher Algebra Galois Theory, has been annotated by Albert A. Blank. ([c]20082005 Book News, Inc., Portland, OR) |
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