Reddit mentions of Abstract Algebra: An Introduction, 3rd Edition

> Hungerford

I assume you're talking about the GTM book that everyone thinks of when they say Hungerford. I'm currently teaching a class out of his other, more elementary abstract algebra textbook:

https://www.amazon.com/Abstract-Algebra-Introduction-Thomas-Hungerford/dp/1111569622

That might be more what you're looking for. Polynomial rings are discussed in chapters 4 and 5. Chapter 4 does the basic division algorithm/unique factorization/irreduciblity criteria from a very hands on perspective. Chapter 5 is polynomial modular arithmetic and F[x]/(p(x)).

Ideals and quotient rings in general aren't introduced until Chapter 6, Euclidean domains/UFDs/PIDs don't come up until chapter 10. Homomorphisms show up briefly in Section 3.3, but they aren't really used much in chapters 4 and 5.

Hungerford's Abstract Algebra is seen at my university as the best book for Abstract Algebra. This is mostly due to the fact that he covers Ring Theory before covering Groups. My university teaches Algebra this way, covering Rings before groups. However, Hungerford conveniently includes a study plan in his book for covering Groups before Rings. In my opinion, Hungerford has a great book with plenty of examples and exercises, with additional sections on applications.

Edit: Sorry, should have included what textbook I was talking about. It's fixed now!

I really enjoyed going through Abstract Algebra: An Introduction by Hungerford. There is an option to begin with Group Theory or begin with Ring Theory, if that's important to you. I think Hungerford's book is a very good introduction with plenty of exercises.