Looking for an Algebra Textbook with References to Number Theory and Topology?

[Pippi]

I am looking for a good textbook that can help developing intuition in algebra. I know a bit of number theory (Fermat's little theorem), algebra (up to fields), and topology. Are there good books that teach algebra with references to number theory and topology?

I learned from Artin's textbook (up to chapter 5). It has no number theory at all and provides too little intuition for me.

 

[mathwonk]

the chapter 11 on factorization in artin is related to number theory, as is the chapter 14 on galois theory, and chapter 8 on linear groups is related to topology. I suggest you keep going in artin. there are very few algebra books of that quality out there, in fact that may be the best there is. you have only gotten 1/3 of the way through it.

if you want a more elementary book that explicitly sets out to do number theory by abstract algebra, there is one by ethan bolker, but i have not seen it.

there are some books that relate algebra more to number theory and topology, but it is possible they will be over your head until you finish artin, but that is not certain.

some examples are: theory of algebraic numbers, by e. artin; introduction to algebraic topology, e. artin and hel braun;
theory of algebraic functions of one variable, chevalley.

why don't you go to a library and look up these books and browse around a bit. you might find what you are looking for.

 

[Studiot]

The book simply entitled 'Algebra' by Archbold may well answer your needs, although you have given us precious little to go on.

It is an old book so it contains many examples and worked tricks, not shown in modern texts.
It's emphasis is on working things out, rather than a Euclidian diet of
definition> lemma> theorem>definition>lemma>theorem...