Is Serge Lang's famous book Algebra nowadays still worth reading, or are there other, more modern books which are better suited for an overview over all areas of algebra?

EDIT: My main concern is that the first edition of Algebra is already 48 years old. Even if there have probably been no fundamental new insight in Algebra which can be included in a first-year-graduate algebra course, the passage of the decades may have helped clarify what are the most important results and techniques as well as how they can be achieved with the least effort.

In addition, I'm wondering whether the terminology and notation is nonstandard or out of fashion (for example Lang, calls integral domains entire rings, an expression which I have never seen anywhere else).

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    $\begingroup$ I like this question, but feel that you should probably edit it to include some properties of a book that makes it "worth reading" to you, to prevent anyone from voting to close as "not constructive". (e.g. relevance to modern undergraduate courses, lots of examples, emphasises rigour rather than intuition or the other way round.) $\endgroup$ Apr 7 '13 at 20:44
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    $\begingroup$ "Take any book on homological algebra, and prove all the theorems without looking at the proofs given in that book." -Serge Lang, Algebra $\endgroup$ Apr 7 '13 at 20:47
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    $\begingroup$ Hmmm... don't you think this question will likely solicit debate, arguments, polling, or extended discussion? Is this one of the practical, answerable questions based on actual problems that you face? $\endgroup$ Apr 7 '13 at 20:48
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    $\begingroup$ @ZevChonoles: I think it is a practical question because I'm asking whether I should read this doorstopper or other algebra books. It's answerable in the sense that you can say either "Yes, it's still perfectly up to date" or "No, there are other Algebra books which incorporate newer viewpoints that make it easier to get used to the matter. $\endgroup$
    – Dominik
    Apr 7 '13 at 21:52
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    $\begingroup$ @Dominik: Those are opinions, not answers. The natural result of your question is some people saying "Yes Lang is worthwhile" and other people saying that <my favorite book> is totally better, because it does all of these new things, and then the first group claiming that those "new viewpoints" are present in Lang already, or not interesting, or not necessary to learn now, etc. Jasper's answer has averted this by simply taking both sides and making a long list of most modern algebra textbooks, thereby appeasing everyone. This does not change the fact that your question is entirely subjective. $\endgroup$ Apr 7 '13 at 22:45

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  • $\begingroup$ "cite" feature here is so useful. $\endgroup$
    – user624723
    Oct 22 '19 at 13:38

Algebra by Serge Lang is still widely used as a course text in many graduate schools.

For a great alternative, try Basic Algebra I and Basic Algebra II by Nathan Jacobson, or Basic Algebra and Further Algebra and Applications by Paul Cohn.

For more modern material, try Graduate Algebra: Commutative View and Graduate Algebra: Noncommutative View by Louis Rowen, or Basic Algebra and Advanced Algebra by Anthony Knapp.

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    $\begingroup$ I highly recommend that anyone using Lang's Algebra should also have at hand George Bergman's superb Companion to Lang's Algebra. Its two-hundred odd pages fill in many of the gaps and provide much supplementary content. $\endgroup$
    – Math Gems
    Apr 7 '13 at 20:57
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    $\begingroup$ I completely agree-and Berman's wonderful new text on universal algebra from the standpoint of category theory will make a terrific followup. $\endgroup$ Apr 22 '15 at 3:06
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    $\begingroup$ @user4594 These are all very good recommendations,but Paul Cohn's books have always troubled me. While they're very nicely written,they're almost comically concise. I don't know how anyone could actually learn algebra from them. As abstract as Lang's book is,at least it has lots of examples. There are almost none in Cohn. If used alongside a more concrete and detailed treatment-such as Vinberg's comprehensive and wonderfully concrete text-their union could certainly be the basis for a strong graduate algebra course. If I could only have one book,my choice would be Aluffi's beautiful text. $\endgroup$ Jul 11 '16 at 3:46
  • $\begingroup$ @Mathemagician1234 by "Berman's wonderful new text" which book are you referring to? $\endgroup$
    – athos
    Dec 31 '18 at 0:09
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    $\begingroup$ @athos I guess it's a reference to An Invitation to General Algebra and Universal Constructions $\endgroup$ Jan 20 '20 at 15:16

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