What is a good Algebra reference text?

Question

I'm looking for a reference text with classic results in algebra, like

Fundamental theorem of finitely generated abelian groups
Every field has a unique smallest prime field, which is either $\mathbb{F}_p$ for some prime $p$ or $\mathbb{Q}$.
Every two $K$-vector spaces with isomorphic bases [as sets] are isomorphic [as vector spaces] (NOT just the finite case)

I want something to cite for a class project. I have Lang's Algebra, and like it, but it seems some of these things are too basic for him. Artin's Algebra doesn't seem to have the infinite case of the last point (maybe I just didn't look carefully).

Is there anything that's organized in encyclopedic fashion like Wikipedia?

Three related threads: Requesting abstract algebra book recommendations, Good abstract algebra books for self study, Casual book for abstract algebra — t.b., Dec 07 '11 at 10:14
http://www.ocf.berkeley.edu/~abhishek/chicmath.htm#i:general-abstract-algebra — Karatuğ Ozan Bircan, Dec 07 '11 at 19:35
"Basic Algebra" by Knapp may be the best for your modest needs. — Mark, Dec 07 '11 at 22:19
@KaratugOzanBircan : I think Mathematics 250A from Ken Ribet is useful, too. Here is the link to it: Maths 250A — trequartista, Dec 08 '11 at 04:07
@KaratugOzanBircan, thanks, the MacLane book looks interesting. — gatoatigrado, Dec 08 '11 at 04:56

score 11 · Accepted Answer · edited Dec 07 '11 at 19:12

11

Abstract Algebra from Dummit and Foote is a very nice abstract algebra book which covers a lot but not as general as Lang's Algebra.

edited Dec 07 '11 at 19:12

bzc

8,778

answered Dec 07 '11 at 10:11

Noud

543

trequartista · Answer 2 · 2011-12-08T03:27:49.950

4

Absolutely agree with Jwaixs, but on the other hand I think Abstract Algebra by Jean Antoine Grillet, GTM 242, Springer is also a good one(it provides something that are not included in the other textbook, like hereditary ring, etc..), especially if you can do all the exercises :D

edited Dec 08 '11 at 03:27

answered Dec 08 '11 at 02:02

trequartista

1,377

2

I consider Grillet to be the best one-volume text for a graduate algebra class that currently exists. Much shorter,more readable and focused then Lang and very similar in spirit. – Mathemagician1234 Dec 08 '11 at 02:57
I agree, Grillet is my favourite Abstract Algebra book, by far. It isn't perfect, but it's much better, IMO, than Lang, Rotman, Knapp, Aluffi, Hungerford, Dummit&Foote, etc. – Leo Dec 10 '11 at 17:54
@LeonLampret : I think Dummit & Foote is better for beginner than Grillet's one. Both books have its own advantages and in my opinion, they are both best books on Abstract Algebra. – trequartista Dec 11 '11 at 04:50

alpha.Debi · Answer 3 · 2011-12-14T08:48:08.437

0

The author Prof. Louis Rowen has excellent level books in Abstract Algebra: Group theory, Ring theory , Rings with Polynomial Identities, etc.

edited Dec 14 '11 at 08:48

answered Dec 08 '11 at 07:29

alpha.Debi

1,094

What is a good Algebra reference text?

3 Answers3

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