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I want to have a book I can use to look up things - The problem I have with most books is that when I want to read a theory about something I usually have to read some background first. And it is really unhelpful if the author puts some "blank spots" in the proofs where he says that the reader should prove it himself. I want to have a book that even proofs the most trivial things like commutativity or associativity or something like that.

I hope somebody can give me a good book which build up from the basics like serge lang's algebra book but really proves everything.

I want to read it quickly. Understand one thing and immediatley go to the next thing without pondering about it too long.

The issue is that often things can be proven much more easily when using a more advanced methode therefor it does not make sense to spend too much time with the basics there is no benfit to it in my opinion.

German would be great.

New2Math
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  • Perhaps the books mentioned in the comments on this post: https://math.stackexchange.com/questions/1130854/elementary-algebra-book-for-review-revision?rq=1 might help! – EBP Jun 01 '20 at 07:27
  • If I understand you correctly, you want something that has content at the same level of sophistication as Lang's Algebra (i.e., theorems at the same level), but you want the proofs to be very detailed? You could use Bourbaki's Algebra and Commutative Algebra, and just leave out the exercises. A tremendous amount of care went into the writing of these books. In practice, most people who don't have at least some background in abstract algebra will find it difficult to learn that way, however, mainly because the material is ordered strictly from most to least general. – Anonymous Jun 01 '20 at 21:48

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