Grad Algebra 1 & 2 Textbook: Amazon Reviews and Advice

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cap.r
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hey I am going to take the graduate algebra 1 and 2 classes as an undergrad and am trying to buy a book and start reading to be prepared.

algebra 1 is listed to include
Groups with operators, homomorphism and isomorphism theorems, normal series, Sylow theorems, free groups, Abelian groups, rings, integral domains, fields, modules. Topics may include HOM (A,B), Tensor products, exterior algebra
the recommended book is https://www.amazon.com/dp/0471433349/?tag=pfamazon01-20

same book for algebra 2 but the topics are
Field theory, Galois theory, multilinear algebra. Further topics from: Dedekind domains, Noetherian domains, rings with minimum condition, homological algebra

so should I just go with that book or is there a good classic text I can use for self study and just buy this one if the prof assigns homework from it. from the reviews it seems to be a solid book and even for self study it should be good. just wanted to hear what you guys think.


thanks
 
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wow good stuff thanks for the link. I actually ordered it off amazon to encourage him to keep writing stuff and making it public. the book has so much material in it I will be referencing to it for years. and for only $18 it's a no brainier it would cost that much for me to print and bind the pages myself
 
I would recommend Saunders Mac Lane's book simply titled Algebra for your purposes. It covers the majority of what you are looking for in depth and rigor, introducing also categories.

Also, it is one of the only general algebra books that I know of that covers multilinear algebra; most others seem to cover only linear.