Basic Abstract Algebra: For Graduate Students and Advanced Undergraduates (Dover Books on Mathematics) | 
 enlarge | Author: Robert B. Ash
Publisher: Dover Publications
Category: Book
List Price: $22.95
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Rating:  2 reviews
Sales Rank: 603038
Media: Paperback
Pages: 432
Number Of Items: 1
Shipping Weight (lbs): 1.2
Dimensions (in): 9.1 x 6.4 x 1
ISBN: 0486453561
Dewey Decimal Number: 512.02
EAN: 9780486453569
Publication Date: December 1, 2006
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Product Description
This survey of fundamental algebraic structures employs techniques applicable to mathematics, physics, engineering, and computer science. Topics include relations between groups and sets, the fundamental theorem of Galois theory, and the results and methods of abstract algebra in terms of number theory, geometry, and noncommutative and homological algebra. Solutions. 2006 edition.
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| Customer Reviews:
 Intuitive Algebra June 19, 2007
Math Buff
16 out of 16 found this review helpful
This is the book version of a series of lecture notes on abstract algebra written by the author and still available on his web page. However, given the price (it's a Dover book...) it's worth buying just to avoid that thick pile of sheets lying around. The best thing about this book is that it avoids formalism whenever it can without sacrificing rigor. Many theorems are "proved" by means of an example of a general case. In this way, the reader gets the intuition behind the result without having to deal with the abstract and sometimes artificial constructs of a rigorous proof. In any case, supplying that rigorous proof can be seen as an extra exercise (or you can look it up elsewhere!). In other words, it's a great book to learn the ideas behind the theorems dealing with groups, rings, modules and fields.
The second part of the book deals with commutative algebra, algebraic number theory, algebraic geometry and homological algebra - areas where it's very hard to find intuitive explanations in the literature, since books on those subjects tend to assume (quite reasonably) the reader has a solid background in abstract algebra. Unfortunately, that means that examples and intuitive explanations are drastically reduced, sometimes to none at all. That makes this book even more attractive.
In any event, after you get the intuition, it will be much easier to to tackle the more rigorous approaches of Dummit & Foote or Hungerford (I don't know Lang's book but I'm told it's much dryer than these two).
Or you can start your study of algebra with any of these more traditional books and use Ash's as a supplement. If a theorem or its proof proof seems opaque, look it up on Ash. Chances are his explanation will clarify things.
 An average resource October 23, 2007
A. Kaszubowski (Altoona, WI USA)
0 out of 2 found this review helpful
I used this book as a reference resource for an advanced algebra course. At times, wording of key concepts was a little long. This book is a good complementary reference to Joseph Gallian's Contemporary Algebra book.
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