🧵 Book recommendation request
Anonymous at Sun, 10 Mar 2024 17:15:04 UTC No. 16066634
Hello sci.
I am an undergrad student, struggling A LOT with commutative ring theory (the stuff in Artin Algebra chapter 11 12 13 15).
I am struggling with problems of factoring stuff in a ring, finding which two given rings are isomorphic and in general i have been unable to develop intuition for the subject
I studied group theory from Keith Conrad's notes, Rotman an Introduction to the Theory of Groups, Herstein Topics in Algebra, and Martin Isaac finite group theory and liked them a lot
But I have not found similar resources for ring theory. Should i just do Herstein and call it a day?
Any good books /prerequisites/pathways to develop a strong intuitive familiarity and deep understanding of this topic?
Anonymous at Sun, 10 Mar 2024 17:39:58 UTC No. 16066683
Books are for nerds
Anonymous at Sun, 10 Mar 2024 17:49:45 UTC No. 16066701
I'm quite fond of Gorodentsev's Algebra books. Really great problems too
Anonymous at Sun, 10 Mar 2024 17:51:55 UTC No. 16066705
>>16066634
For very general ring theory I suggest:
Hungerford Algebra (lots of examples, exercises, use of categories etc.) or Lang (more terse, but Lang is a love it or hate it, you might like his overview of rings and his exposition).
More advanced would basically be Atiyah-Macdonald or Matsumura for commutative algebra. Work a lot of exercises always, don't just look up answers etc.
Anonymous at Sun, 10 Mar 2024 17:53:28 UTC No. 16066708
>>16066634
Lang
Anonymous at Sun, 10 Mar 2024 18:06:16 UTC No. 16066724
>>16066705
>>16066708
Lang and Hungerford do it with non commutative rings and left/right ideals, also Hungerford helped me a lot in group theory but somehow I just could not get into the categorical treatment,
So now that it has come to this
Will hungerford/lang help me do those Artin pronlems of factoring this in this, or is R/I isomorphic to R' type of problems
Anonymous at Sun, 10 Mar 2024 18:07:18 UTC No. 16066725
>>16066724
Also, how to do category theory, many people told me about Aluffi algebra chapter 0, what should I do for category theory basics to use it in groups/rings etc basic algebra
Anonymous at Sun, 10 Mar 2024 18:58:20 UTC No. 16066808
Try Sharpe Rings and Factorization
It doesn't go more brainlent than that
Anonymous at Sun, 10 Mar 2024 19:38:48 UTC No. 16066868
>>16066634
Mir Titles
scares the westoid
Anonymous at Sun, 10 Mar 2024 20:25:38 UTC No. 16066940
>>16066808
I am not even that stupid bro I need something like Rotman Group Theory, Martin Isaac Finite group theory and keith conrad group theory notes
Anonymous at Sun, 10 Mar 2024 20:26:41 UTC No. 16066944
>>16066868
Wtf I searched it and nothing is coming
Anonymous at Sun, 10 Mar 2024 21:07:00 UTC No. 16067019
>>16066725
For cat theory I like Borceaux's books
Anonymous at Mon, 11 Mar 2024 11:54:09 UTC No. 16067971
>>16066944
https://archive.org/search?query=mi
Anonymous at Mon, 11 Mar 2024 16:44:12 UTC No. 16068347
>>16066634
If you're German, Gerritzen's book is short and great for a quick overview of algebra
Anonymous at Mon, 11 Mar 2024 18:55:48 UTC No. 16068715
>>16066634
Matsuura
Anonymous at Mon, 11 Mar 2024 19:05:47 UTC No. 16068732
>>16066634
Grillet is amazing