Alternatives to Dummit and Foote for a text in Algebra

Question

I am reading Abstract Algebra from Dummit Foote.

I need to cover the following topics for my upcoming exam:

Abstract Algebra:

Groups:

Groups, homomorphisms, normal subgroups and quotients, isomorphism theorems, finite groups, symmetric and alternating groups, direct product, structure of finite abelian groups, Sylow theorems.

Rings:

Rings and ideals, quotients, homomorphism and isomorphism theorems, maximal ideals, prime ideals, integral domains, eld of fractions, Euclidean rings, principal ideal domains, unique factorization domains, polynomial rings.

Fields:

Fields, characteristic of a field, algebraic extensions, roots of polynomials, separable and normal extensions, finite fields.

Elementary number theory and combinatorics:

Divisibility, congruences, standard arithmetic functions, permutations and combinations.

However I find that an enormous amount of material has been given in this book and the book also has a great volume.I don't know when will I finish this book.

Is it necessary to cover all the topics related to above from the book?

Are there any alternatives to Dummit Foote as a standard text which also has good problems and exercises and would serve me well on these topics for my upcoming exam allowing me to finish the topics in a reasonable time??

Answer 1

This semester I took a course of "Rings and Modules" (and studied a bit of groups too). I didn't know deeply sereval books of abstract algebra, but between those I've found, I recommended Contemporary Abstract Algebra, of Joseph A. Gallian (I read the ninth edition). I appreciated it for the clarity of proves, the coverage, the exemples, the partial solution manual at the end (it contais answers or hint for old-numbered exercises). Besides, I found all answers for the even-numbered exercices that I needed here, in math.stackexchange.com! These qualities make it a book for self-study, in my opinion. Talking about your wishes, I believe it do suit. I hope you listen students more versed than me and do the best choice!

Answer 2

I have heard of "Fundamentals of Abstract Algebra" by D. S. Malik which has worked solutions of exercises (something quite rare in algebra books).

You may want to try it.

I also recommend Hungerford, however that has the problem of being just as lengthy as Dummit & Foote.

Answer 3

I’m getting to like Dummit & Foote. I agree the book is lengthy. But, it is also very comprehensive, so I keep coming back to it. Hungerford is more terse and a bit more higher level than D&F. Try Lang, “Undergraduate Algebra,” if you want the Cliff Notes on abstract algebra. He goes very fast and doesn’t cover as much material. Lang’s graduate level “Algebra” is the gold standard with the same topics and contents as UG, but at a higher level (60,000 volts)!