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Divided into two sections, this book covers both the standard topics (groups, modules, ...
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.
|Ch. 1||Groups (mostly finite)|
|Ch. 2||Rings (mostly domains)|
|Ch. 4||Vector spaces|
|Ch. 5||Fields and Galois theory|
|Ch. 6||Topics in noncommutative rings|
|Ch. 7||Group extensions|
|Ch. 8||Topics in Abelian groups|