Which abstract algebra textbook is most cummulative

[aLearner]

If I were to use an abstract algebra book for quick and easy reference which one would it be? Dummit and Foote is very cumulative, is there anything better in the market? And how long would it take to work out all of D + F for an average student with basic background in Algebra?

 

[rasmhop]

What does it mean to you to work out all of D+F? You could probably go through it in a semester or so if you kept at it and come out with a decent understanding (most people spread it out over a longer period though with other classes in between and I believe this is a better way to learn algebra), but you will only truly gain an understanding of it when you study other math and use the algebra in various ways and comes back to see a subject in a new light. If you have started with D+F you may have already encountered group actions and you may be able to solve the exercises, do some basic counting and list of the axioms, but you will not truly understand how significant and powerful this simple abstraction is till you have seen it strecthed in various ways in applications.

As for what is most "cummulative" I don't think there is a standard way to measure that, but I think Serge Lang's algebra (the GTM version of course) is the best answer without further context. However it is considerably harder than D+F and should in my opinion mainly be used when you are curious about a certain topic, not when you want to learn a lot of different algebra. However D+F is plenty comprehensive, and alternatives like Rotman's Advanced Modern Algebra are probably at about the same level as D+F but with a slightly different focus.

In the end I don't think knowing what books are "cummulative" is going to do you much good.

 

[aLearner]

I definitely will be taking Linear Algebra and I'm using the book to gain command over Shankar's Principle's of Quantum Mechanics and J.J Sakurai's Quantum Mechanics. But more so, plenty of physical sciences use groups to explain theory, and so I truly believe a really strong foundation on the topic is essential. I'm no expert, but I am aware of its capabilities, which is another reason why I'm fascinated about it. I have every intention of applying it on certain ideas that have been boiling up in my mind, but before I dive into it I want to make sure that my intuitions are strong. I don't want to take it up as a "come back to it when you are stuck" book because I consider it as essential to higher learning as basic algebra was to college sciences. A semester sounds like a real short period of time to work out all the problems, but I could try that anyway. Thanks for responding.