A First Graduate Course in Abstract Algebra [Hardcover]

Since abstract algebra is so important to the study of advanced mathematics, it is critical that students have a firm grasp of its principles and underlying theories before moving on to further study. To accomplish this, they require a concise, accessible, user-friendly textbook that is both challenging and stimulating. A First Graduate Course in Abstract Algebra is just such a textbook.

Divided into two sections, this book covers both the standard topics (groups, modules, rings, and vector spaces) associated with abstract algebra and more advanced topics such as Galois fields, noncommutative rings, group extensions, and Abelian groups. The author includes review material where needed instead of in a single chapter, giving convenient access with minimal page turning. He also provides ample examples, exercises, and problem sets to reinforce the material. This book illustrates the theory of finitely generated modules over principal ideal domains, discusses tensor products, and demonstrates the development of determinants. It also covers Sylow theory and Jordan canonical form.

A First Graduate Course in Abstract Algebra is ideal for a two-semester course, providing enough examples, problems, and exercises for a deep understanding. Each of the final three chapters is logically independent and can be covered in any order, perfect for a customized syllabus.PREFACE
GROUPS (MOSTLY FINITE)
Definitions, Examples, Elementary Properties
Subgroups, Cyclic Groups
Factorization in Z
First Problem Set
Isomorphism
Second Problem Set
Homomorphisms
Third Problem Set
Normal Subgroups and Factor Groups
Fourth Problem Set
Simple Groups and Composition Series
Fifth Problem Set
Symmetric Groups
Sixth Problem Set
Conjugacy Classes, p-Groups, Solvable Groups
Seventh Problem Set
Direct Products
Eighth Problem Set
Sylow Theorems
Ninth Problem SlÓ-