Good textbooks for Group,Ring,Field Theory

Asked Dec 31 '18 at 09:17

Active Dec 31 '18 at 09:17

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This is in reference to this:Good abstract algebra books for self study.

I am an undergraduate student in Mathematics.I have studied Introductory courses in Ring Theory and Group Theory.

I would like to study the following courses:

Group Action,Stabilisers,Cayleys Theorem,Class Equation,Automorphisms,Direct Products,Solvable Groups,Simple Groups in particular $A_n$.
Field Theory: Algebraic Extension,Algebraic Closure,Finite Fields.
Galois Extension,Cyclotomic Extensions ,Solvability of radicals.
Ring Theory:Euclidean Domain,Principal Ideal Domain,UFD.

I want a book which can be used as a textbook

I checked out the above references which mainly asked to study Dummit Foote.

But I found Dummit & Foote too broad.Its fine as reference though.Lang is quite tough.Artin does not cover all the topics and is more intended towards Geometry.Gallian is nice but cant be used as a textbook.

I want a book like "Bartle and Sherbert of Real Anlaysis" which can be used as a textbook and

What are some

asked Dec 31 '18 at 09:17

Try Herstein's "Topics in Algebra" as suggested in the comments section of the question referred to in your link. – John Douma Dec 31 '18 at 09:21
1

You can try Aluffi’s “Algebra, Chapter 0”. – Aurel Dec 31 '18 at 09:25
Im starting now the book of Aluffi, it seems better that many other classic texts – Dec 31 '18 at 09:46
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Jacobson's Basic Algebra – YuiTo Cheng Jan 01 '19 at 11:41

Good textbooks for Group,Ring,Field Theory

0 Answers0