# Lang as a first algebra book

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

• with that background, you don't need hesitate – janmarqz Jan 2 '14 at 3:46
• You can answer your question by simply opening the book and reading it. You'll realize immediately if it suits you or not. – Pedro Tamaroff Jan 2 '14 at 3:47
• Indeed, Lang's style is nice in that the moment you begin reading it, you know if you're mature enough for his text or not. – mathematics2x2life Jan 2 '14 at 3:54
• For what it's worth, I recommend Joseph Rotman's Advanced Modern Algebra. goo.gl/jUkvFM – Sammy Black Jan 2 '14 at 4:09
• For addition reference consider this community wiki post, Is Serge Lang's Algebra still worth reading?. – cyclochaotic Jan 2 '14 at 16:31

There are many rough spots in Lang's exposition (along with many great insights). But it is easy to remedy these deficiencies. George Bergman has written a superb $\,$ Companion to Lang's Algebra.  Its two-hundred odd pages fill in many of the gaps and provide much supplementary content. Combined you have an algebra textbook written by two leading algebraists - which is quite rare.

That said, I highly recommend that you learn from at least a few different textbooks. You might find it helpful to go to your university library and browse various algebra textbooks to get a feel for the level of exposition, the optional topics treated, the breadth and depth of exercises, etc.

• Agreed on this. I think if you're prepared for it and like the style, Lang's book is still the best place to learn Algebra, but there are better references for further reading now than the ones he gives. – Callus - Reinstate Monica Jan 2 '14 at 4:10
• Great, I can't wait. Thanks everyone! – NeurallyInspired Jan 2 '14 at 6:57