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I have been suggested Artin or Herstein's books. What do you think is more rigorous but at the same time clear and good to read?

Jean-Claude Arbaut
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user62029
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  • For a clear, fun to read text, I highly recommend Pinter's "Book of Abstract Algebra". It is not rigorous, however. But it is absolutely loaded with exercises. I personally love it – Patrick Shambayati Sep 19 '14 at 20:01

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Lang's Algebra is very nice, and van der Waerden (vol1, vol2) is the best I know of, together with Mac Lane & Birkhoff. I find the latter significantly harder to follow. There is also Dummit & Foote, at a level equivalent to Lang.

I don't own Artin's Algebra, but I'd say it's also at the level of Lang, and it has a very good reputation.

Edit: the other books I have are of Emil Artin. The Artin whose lectures the books by van der Waerden were originally based on (see here on Wikipedia). Michael Artin is actually his son, and is probably the author you are refering to.

Jean-Claude Arbaut
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  • @user62029 I edited the answer, since I didn't pay much attention: there are two Artin, both well known in algebra :-) – Jean-Claude Arbaut Sep 19 '14 at 20:15
  • I think both Lang's and MacLane's books can be terrible for a beginner. Much better, imo, Dummit & Foote. Van der Waerden's already too old, imo again. – Timbuc Sep 19 '14 at 20:17
  • @Timbuc Agreed for MacLane & Birkhoff, which is quite hard, but I don't agree about Lang, I found it very clear, and I actually prefer it other Dummit & Foote. Matter of taste, since they are, I think, almost on the same level. – Jean-Claude Arbaut Sep 19 '14 at 20:23
  • I think Lang is even worse than MacClane's for a beginner: it is way too dry, abstract and almost without examples...and it assumes already a lot as it is a graduate text. Perhaps you're thinking of Lang's Undergraduate Algebra ? – Timbuc Sep 19 '14 at 20:27
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    Lang is terrible for a student. Go with Dummit and Foote. – David P Sep 19 '14 at 20:28
  • @Timbuc No, I had really Algebra in mind. Maybe I'm biased since I started with it after I finished my student life. However, having both today (and actually all I mentioned), I still don't agree. Just my humble opinion! – Jean-Claude Arbaut Sep 19 '14 at 20:33
  • @Jean-ClaudeArbaut, anyway: Lang's "Algebra" ios for graduate level. – Timbuc Sep 19 '14 at 20:53
  • @Timbuc According to reviews, D&F is for advanced undergraduate or graduate, and I can only confirm they are more or less on the same level, IMO. I guess we could argue endlessly about it. Just an example: both Lang and D&F are used for graduate algebra at Stanford (see here) Maybe not the best example, since the prof. finds D&F a better text, and Lang for encyclopedic reference, but anyway... – Jean-Claude Arbaut Sep 19 '14 at 21:06
  • Thanks for the answer and all the comments. – user62029 Sep 27 '14 at 21:09