AlgebraAddison-Wesley, 1993 - 906 pages This basic text for a one-year course in algebra at the graduate level thoroughly prepares students to handle the algebra they will use in all of mathematics. The author assumes that students have a basic familiarity with the language of mathematics "i.e.: sets and mapping, integers, and rational numbers." The text was thoroughly revised and enhanced in response to reviewers' comments and suggestions. Designed to improve students' retention and comprehension, the text is divided into four parts. The first introduces the basic notions of algebra. The second covers the direction of algebraic equations, including the Galois theory, and the final two parts cover the direction of linear and multilinear algebra. |
Table des matières
Part One The Basic Objects of Algebra | 1 |
Groups | 3 |
Groups | 7 |
Droits d'auteur | |
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Expressions et termes fréquents
A-module a₁ abelian group absolute value algebraically closed algebraically independent assume automorphism b₁ basis bilinear called Chapter character closure coefficients commutative ring concludes the proof conjugate contained Corollary coset decomposition define degree denote diagram dimension direct sum E₁ embedding equal exact sequence Example Exercise F₁ factor field finite dimensional finite extension finite free finite number follows free module function functor G₁ Galois group given group G Hence homogeneous homology homomorphism induced injective inverse irreducible irreducible polynomial isomorphism kernel left ideal Lemma Let f Let G linear map matrix maximal ideal monoid morphism multiplicative Noetherian non-zero positive integer prime ideal prime number Proposition prove representation roots of unity semisimple Show subfield subgroup of G submodule subset Suppose surjective symmetric tensor product Theorem trivial unique unit element v₁ variables vector space verified write x₁ zero