A first graduate course in abstract algebra

W.J. Wickless9780824756277, 0824756274

Graduate textbooks often have a rather daunting heft. So it’s pleasant for a text intended for first-year graduate students to be concise, and brief enough that at the end of a course nearly the entire text will have been covered. This book manages that feat, entirely without sacrificing any material coverage. The standard topics of group theory, vector spaces, modules, rings, field and Galois theory are covered, as well as topics in noncommutative rings, group extensions, and selected topics in abelian groups. Some of the brevity is a result of the fact that instead of providing large chunks of exercises of middling difficulty, Wickless (math, University of Connecticut) has opted to provide fewer exercises of greater difficulty.

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Table of contents :
Preface……Page 10
Contents……Page 12
Groups (mostly finite)……Page 16
Rings (mostly domains)……Page 64
Modules……Page 90
Vector spaces……Page 110
Fields and Galois theory……Page 158
Topics in Noncommutative Rings……Page 190
Group extensions……Page 206
Topics in abelian groups……Page 222
References……Page 244
Index……Page 245