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I have studied analysis up to Rudin's Real and complex Analysis level and read Munkres' Topology book, and now I have decided to study abstract algebra. I am trying to decide between Artin's Algebra, Dummit & Foote's book and Herstein's Topics in algebra. My only knowledge of algebra comes from Hoffman & Kunze's book which I read about a year ago, so I would like to know if a solid understanding of linear algebra is required to read this books.

In short, which book is best for someone who doesn't know much algebra but has studied analysis more thoroughly and topology at a decent level?

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  • $\begingroup$ Any of the books you listed should be readable given your background. Dummit and Foote is by far the most comprehensive of the three, but it's a bit dry, like reading an encyclopedia (in my opinion). Herstein's is a lot more fun to read, for the topics it covers. You don't need all that much linear algebra to study groups, rings, and fields (just a bit for field theory). H&K should be adequate preparation. $\endgroup$ – Bungo Sep 10 '15 at 20:36
  • $\begingroup$ Thanks! I guess I'll read Herstein's since I don't care about completeness that much for a first read. $\endgroup$ – Aitor Ormazabal Sep 10 '15 at 20:40
  • $\begingroup$ One thing about Herstein to keep in mind, if you are planning to do the exercises: some of the exercises are quite hard (with stars indicating difficulty), often because he likes to present them as soon as you are able to understand the question, but before you have the tools (developed in subsequent chapters) to tackle it in the "standard" way. This can be good, because you will appreciate how powerful the tools are once you have them, but it can also be frustrating if self-studying. So don't be afraid to skip the starred exercises as needed. $\endgroup$ – Bungo Sep 10 '15 at 20:46
  • $\begingroup$ I will keep that in mind, thanks $\endgroup$ – Aitor Ormazabal Sep 10 '15 at 20:55

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