Advanced Modern Algebra: Third Edition, Part 1 (Graduate Studies in Mathematics)

Description

Part One--this volume--can be used as a text for the first year of graduate algebra, says Rotman, but it and the forthcoming Part Two can also serve more advanced graduate students wishing to learn topics on their own. They comprise a reference as well, he says, containing many of the standard theorems and definitions that users of algebra need to know. Part One contains material for two courses. The first course covers classical formulas, classical number theory, commutative rings, groups, and Galois theory. The second course covers modules, Zorn's lemma, advanced linear algebra, categories of modules, multilinear algebra, and more commutative algebra. Annotation ©2016 Ringgold, Inc., Portland, OR (protoview.com) Review: Five Stars - great Review: not remotely as good as the second edition - Compared to the second edition, this has the following disadvantages: 1. Poor overall organization. The author assumes that you know what a group is, even saying explicitly that because this is a graduate text, you can be assumed to know what a group is. Then in the groups chapter (which is *after* the chapter on rings), he tells you all over what a group is. I think he just wanted to reorganize the second edition for some mysterious reasion. It was much clearer before. 2. Typos. Just sloppy. On p.87, for example, it says, "In Example A-3.105, we exhibited eight monic irreducible ..." but A-3.105 does not appear until p.91! There has clearly been serious cutting and pasting from previous editions (where the example does precede the text in question). There are also numerous typos scattered throughout. 3. Two volumes instead of one. So effectively much more expensive. Compared to the second edition, this edition has the following advantage: 1. It's in print. I bought it only because I've used my copy of the second edition so much that it's falling apart. Can't decide whether to return it or not but leaning toward sending it back.