Algebra

Serge A. Lang

900 pages, parution le 13/01/1995 (3^eme édition)

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Résumé

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.

Now includes a description of all characters of GL2 of a finite field, which is also woven throughout the book in several contexts.

Elimination theory now complements the existing section on the resultant.

Mackey's theorems include representations of finite groups.

Commutative algebra and noetherian rings have been integrated with elimination theory and algebraic sets.

All the homological algebra now appears in the final part.

The text is designed to enhance your students' retention and comprehension. Lang divides the text into four parts:

The first introduces the basic notions of algebra
The second covers the direction of algebraic equations, including the Galois theory .
The final two parts cover the direction of linear and multilinear algebra.

Table of Contents

I. THE BASIC OBJECTS OF ALGEBRA GROUPS.
Groups.
Rings.
Modules.
Polynomials.
II. ALGEBRAIC EQUATIONS.
Algebraic Extensions.
Galois Theory.
Extensions of Rings.
Transcendental Extensions.
Algebraic Spaces.
Noetherian Rings and Modules.
Real Fields.
Absolute Values.
III. LINEAR ALGEBRA AND REPRESENTATIONS.
Matrices and Linear Maps.
Representation of One Endomorphism.
Structure of Bilinear Forms.
The Tensor Product.
Semisimplicity.
Representations of Finite Groups.
The Alternating Product.
IV. HOMOLOGICAL ALGEBRA.
General Homology Theory.
Finite Free Resolution.
Appendices.

Caractéristiques techniques

	PAPIER
Éditeur(s)	Addison Wesley
Auteur(s)	Serge A. Lang
Parution	13/01/1995
Édition	3^eme édition
Nb. de pages	900
Couverture	Relié
Intérieur	Noir et Blanc
EAN13	9780201555400