I would like to find an algebra book that would suit my needs. It should be advanced graduate/graduate level. I have some experience in group and ring theory but zero in linear algebra.
I'm not scared of graduate books IF there is no prerequisite material on linear algebra and so on(some books are meant as graduate in a sense that they require some mathematical maturity, others assume some undergraduate topics, the latter wouldn't suit me ).
So, my ''ideal'' book would:
1) Go for groups $\to$ rings $\to$ modules $\to$ vector spaces or groups $\to$ rings $\to$ fields $\to$ modules/vector spaces sequences.
2) Not be too long. Well, I don't ask for 200-300 pages text, but something like 500-600. That said, it is desired, but not essential, if the book has other advantages.
3) I'd like it to be modern, that is, released within 20 years before now. But this is not highly essential for me.
4) The book might introduce some category theory language. But it shouldn't cloud the main topic's exposition.
I've started studying Algebra with Aluffi's book, which is a really good book, but, of course, have some flaws. Now I want to try something else, something a little different.
I heard Grillet wrote a really good book, but as far as I'm concerned, it assumes knowledge of linear algebra (which I don't want to learn outside modules/field/ring theory).
I suppose Rotman's Advanced Modern Algebra might suit me, but it's a little too long and has too many topics (which I don't intend to learn just now).
That said, ANY advice would be HIGHLY appreciated. Even if u just came to recommend something that might not suit the conditions above, please, feel free to say, if you think it is worth mentioning (but, please, tell, why do you think a book is so great).