I think I am ready to learn algebra from Lang, but wanted some perspective.
I have been exposed to:
Linear algebra: All of Axler
From my other, legendary honors course:
-Order theory (lattices, partial orders, posets, galois connections)
-Category theory: in the same crazy honors undergraduate analysis course
-Topology: homomorphisms in the category of topological spaces, product topologies, seperation axioms
I have also been exposed to and thought about basic examples of semigroups, involutions, monoids, groups...
My question is, although I own Lang Algebra and absolutely love the style, will it be to my disadvantage to not start with an undergrad book? I suspect that, assuming I'm capable, the graduate treatment would be just fine as long as I'm mature enough. Maybe I'd just get less familiarity with specific examples than I'd get from Artin's book?
Lang himself says in the intro that not having algebra exposure is okay if you have enough mathematical maturity. I'm about to self-study this book, it looks great, I'm just hoping for words of agreement or discouragement (with reasoning!) so that I know it's a good idea.
Lang's book looks so appealing... So please? Can I? =D