# What is a good Algebra reference text?

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?

-
–  t.b. Dec 7 '11 at 10:14
"Basic Algebra" by Knapp may be the best for your modest needs. –  Mark Schwarzmann Dec 7 '11 at 22:19
@KaratugOzanBircan : I think Mathematics 250A from Ken Ribet is useful, too. Here is the link to it: Maths 250A –  N.Z.K Dec 8 '11 at 4:07
@KaratugOzanBircan, thanks, the MacLane book looks interesting. –  gatoatigrado Dec 8 '11 at 4:56
show 1 more comment

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.

-