Last semester I picked up an algebra course at my university, which unfortunately was scheduled during my exams of my major (I’m a computer science major). So I had to self study the material, however, the self written syllabus was not self study friendly (good syllabus overall though).
The course was split up into 3 parts, group theory, ring theory and field theory. As a computer science major we only had to study the first 2.
Now that I passed the exam for this course I want to study the field theory part ( which covers Galois theory, etc).
So, now I want to ask whether any of you know any good books on abstract algebra, which lift off at basic ring theory and continue to more advanced ring theory and to finite fields, Galois theory, …
Please keep in mind that I am not a math major, and that I would like books which are suited for self study (thus a lot of examples and intuition).
Thanks in advance!
There’s always the classic Abstract Algebra by Dummit and Foote. Section II of the text gives a nice treatment of ring theory, certainly providing plenty of review for what you have already covered while introducing more advanced concepts of ring theory. Section III will cover the field and Galois theory you’re interested in. Some of the exercises can be difficult at times, especially for self-study, but the authors tend to give a number of examples and always provide the motivation for why they are doing what they are doing.