Cohn P. Algebra. Vol 2. 2ed 1989 torrent

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Vol. 1 of this work was intended to cover the first two years of an undergraduate course, and there is fairly general agreement on the topics to be included. At the third-year level and beyond there is a much wider range of optional topics, and the element of personal choice enters in a greater measure. The present volume includes a variety of algebraic topics that are useful elsewhere, important in their own right, or that fairly quickly lead to interesting results (preferably all three). To a large extent the selection follows the tradition set by v.d. Waerden's classic treatise, but some departures are clearly necessary, the main ones here being homological algebra, lattices and non-commutative Noetherian rings. The material presented may be grouped roughly into three parts of four chapters each. The first part deals with basic topics: numbers (natural and transfinite), modular and distributive lattices, tensor products and graded rings (with the Golod-Shafarevich theorem as an application) and an introduction to homological algebra. Here 'introduction' means an account which goes far enough to describe Ext and Tor for the category of modules, show their use in group theory and prove the syzygy theorem (a la Roganov), but stopping short of Kiinneth-type theorems or direct and inverse limits. The next part, on fields, has a chapter on Galois theory and one on further field theory, mainly infinite field extensions, but also a little on skew fields. The third part, on rings, begins with valuations, a formal study of divisibility m fields. A chapter on Artinian rings presents the Jacobson theory (radical and semiprimitivity, density theorem) as well as semiperfect rings and a glimpse of group representations, by way of application. It also includes the basic facts on central simple algebras (the Brauer group) and Hochschild cohomology. The chapter on commutative rings emphasizes the links with algebraic geometry and goes as far as the Nullstellensatz. In a slightly different direction, earlier chapters are put to use in a discussion of Dedekind domains and finitely generated modules over them. The final chapter, on Noetherian and Pi-rings, brings Goldie's and Posner's theorems and some of the recent work of Amitsur, Razmyslov, Rowen and M. Artin on rings with polynomial identities.
Preface to the Second Edition
From the Preface to the First Edition
Conventions on terminology
Table of interdependence of chapters (Leitfaden)
Sets
Lattices
Field theory
Modules
Rings and algebras
Quadratic forms and ordered fields
Representation theory of finite groups
Valuation theory
Commutative rings
Coding theory
Languages and automata
List of notations