I've been teaching myself basic (abstract) algebra. I'm not studying for any particular subject. I just want to learn anything that might be useful in the future. Since I have enough time, I treat each part separately. For example, for group theory I'm reading Rotman's An Introduction to the Theory of Groups besides books on abstract algebra. Now I think I know enough group theory to start reading ring theory. I also know basic linear algebra.
I'm looking for an introductory ring theory text on a level similar to that of Rotman's group theory book. However, I don't know what topics a ring theory text shoud include, though I do think that commutative algebra might be too advanced for me now. I have looked through many questions here, e.g. 1, 2, 3, and there are a lot of books listed that look good. However, I'm not sure which book I should read.
I would like to find a book with the following:
- It is introductory and starts from the basics. It does not assume that the reader is familiar things like category theory or homological algebra. It's best if the book spends some time on introducing these.
- It is thorough and comprehensive. I'm a fan of thick books, so I actually like lengthy (but not wordy) books that contain lots of material.
- It is a book on general ring theory (not only commutative algebra).
And please don't recommend texts on abstract algebra, since I already know some good books. I plan to read abstract algebra books concurrently with ring theory texts. :)
Thanks in advance!