Algebra (Graduate Texts in Mathematics, 211)

I covet Lang's algebra for the problem sets. Other writers stoop to conquer, with the hand - holding and low - expectations. Lang expects you not just to understand him but to keep up with him, to not only follow but close the gap. This text is tough-love. His problem sets will terrify initially. They'll bog you down. But they'll help you get your sea legs. His questions, hints and problems are the only ones that consistently provoke me into navigating through an algebraic world of my own making. I would not trade that experience for all the compassion of most other texts. A true algebraist will tell you must get this book. It will remain relevant for a long time.

I really like the book. It can be rough but every time I have sat down and really tried to figure out what Lang is doing in some proof, I come out having learned so much. Additionally, his style really emphasizes the main ideas (which is the most important thing in my mind). Also, there is a lot of supplementary material (eg. Bergman's "A Companion to Lang's Algebra", (just google it)) so it is relatively easy to fill in the details that you get really hung up on. These reasons have made the book my first choice to read up on something that I don't fully grasp. I also really enjoy the random examples he throws in from all over the place. It's pretty cool when you're sitting in class learning something new only to recognize it as that weird example from Lang that you didn't quite understand at the time.

good

It is not often that an author of a graduate textbook shares their understanding rather than merely provide a collection of theorems and proofs. Lang always delivers on this front. I'm partial to analysis myself, so I was certainly hesitant picking up this tome. But you'll find that it has everything you need (and much more). I primarily used the first four chapters, as well as the chapter on algebraic varieties. Each chapter is concise and written in a conversational style. There are many many great exercises as well.

As most of the books written by Prof. Lang, this book is a great compilation, it has what it needs to have, nothing more, nothing less. If you are in Math or any related field, and need a book to refresh your knowledge on Abstract Algebra, this is your book. though, I took a course in Grad School from this book, and I don't recomend it. Fortunatelly I still had the books from my undegrad courses (Rotman's Group Theory book is great), and I did remember the old courses anyway, but I really discourage the usage of this book as a lecture book.

Good graduate level text on abstract algebra. I paired this with sitting in on some lectures in a graduate level course on the subject (Groups and Rings specifically). A lot of proofs/exercises, you get a better feel for it through doing your own proofs and defining your own problems to solve.

This is like an encyclopedia for algebra. You wouldn't want to read it in order to learn the material for the first time, but everything is in there so it makes a great reference.

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C'est un livre qu'on l'utilise pour perfectionner ses acquis après un cours d'initiation ou comme encyclopédie de consultation pour la recherche, ce livre s'avère indispensable.

I love this book. It is, of course, not meant as a first exposure, but it is an amazing read if you are familiar with the basics of algebra. Every time I see some algebraic construction that I'm not familiar with I just look it up in Lang and read some epsilon-neighbourhood of the construction. The point is, the text is SO WELL ORGANISED that you really can learn about constructions and theorems and even general theories etc. very very quickly if you know what it's supposed to be about (i.e. if you don't need 5 pages of motivation and various visualisations etc.). The constructions and arguments leading to theorems and so on are almost always clearly recognisable. Also, great, huge list of references about anything of interest that comes up in the text (more specific references being at the end of the corresponding bits). Even if you don't buy it now, a time WILL COME that you'll want to have this book on your shelf.

It's really an amazing book. The quality of pages, the printing and overall of whole book is good. I definitely suggest to buy this book if you want to invest your time, money & energy in some good book.