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Abstract Algebra (Graduate Texts in Mathematics Book 242) by Pierre Antoine Grillet is a nonfiction available to read on EtoBox.

What is Abstract Algebra (Graduate Texts in Mathematics Book 242) about?

The title of the review pretty much says it all. For a first edition, this isn't bad. I've taken copious notes from this book, and I've learned quite a bit. It's much more comprehensive than most other algebra books on the market, to be sure. I'd be hard pressed to find another introductory algebra book that actually makes it to the Adjoint Functor theorem, tripleability, and Birkhoff's characterization of varieties. However, the book also has its flaws. The most annoying one is probably Lemma 10.6.8 on page 331, which says that a finite dimensional division algebra over an algebraically closed field has dimension 1. This is clearly false. (Consider the quaternions and the complex numbers). The error in the proof is that he assumes commutativity (probably the easiest blunder to make in algebra, so it's a minor offense).Thankfully, no subsequent use of this "lemma" is made in the book (making me wonder why he's choosing to call it a lemma). In some places, Grillet doesn't really have the slickest proof on the market, which would be nice if he's trying to be comprehensive (the book wouldn't be quite as much of a wrist cracker). For instance Jacobson's proof of the simplicity of PSL

Who reads Abstract Algebra (Graduate Texts in Mathematics Book 242)?

Author

Pierre Antoine Grillet

Publisher

Springer US

Published

2007

Language

EN

ISBN

9780387715674

Category

nonfiction

Subjects

Mathematics, Science, Stem

Rating

3 / 5 (3 ratings)

Updated

2026-03-14