Basic Algebra II

✍ Scribed by Nathan Jacobson

• Publisher: Dover Publications
• Year: 2009
• Tongue: English
• Leaves: 681
• Series: Dover Books on Mathematics
• Edition: 2
• Category: Library

✦ Synopsis

A classic text and standard reference for a generation, these two volumes are the work of Nathan Jacobson, an expert algebraist who taught at Yale for over three decades. The books are conceptually and theoretically oriented. Volume one explores all the topics addressed in undergraduate courses, while volume two comprises all of the subjects usually covered in a first-year graduate course, revisiting and expanding on many topics from volume one. Each volume has exercises and insightful, carefully explained proofs.

✦ Table of Contents

Volume I. Introduction : concepts from set theory. The integers --
Monoids and groups --
Rings --
Modules over a principal ideal domain --
Galois theory of equations --
Real polynomial equations and inequalities --
Metric vector spaces and the classical groups --
Algebras over a field --
Lattices and Boolean algebras --
Appendix. Volume II. Introduction --
Categories --
Universal algebra --
Modules --
Basic structure theory of rings --
Classical representation theory of finite groups --
Elements of homological algebra with applications --
Commutative ideal theory : general theory and noetherian rings --
Field theory --
Valuation theory --
Dedekind domains --
Formally real fields.

✦ Subjects

Algebra;Algebra, Abstract;Algebra, Boolean;Algebraic fields;Algebras, Linear;Rings (Algebra)