I am currently an undergraduate student, math major. I am studying abstract algebra, mostly selfstudy. I am using some basic books like Contemporary Abstract Algebra by Gallian etc. Furthermore i am using abstract algebra by Dummit and foote as reference. Recently I saw three interesting books (at graduate level) : Abstract Algebra by Grillet, Advanced modern algebra part 1 by Rotman and Algebra a graduate course by Issac Martin.
I saw books and I felt Rotman's book is too fast and gives little view of groups, rings , fields etc.
On the other hand, Martin's book lacks in category theory. His book doesn't contain category theory. Moreover, I saw online reviews that this book is best for Algebrist. I is true?
When i saw Abstract Algebra by Grillet, this looks me interesting book because author uses category theory in goof amount, Homological Algebra and starts from basic undergraduate Algebra. The only thing book lacks is number of exercises. Grillet's book doesn't have many exercises as Rotman , Dummit and foote. Since this book looks me interesting in first view I wanted to read it.
MY QUESTION: Is the abstract algebra by grillet book is worthy? Is it suitable for me to use it as reference beside D&F abstract algebra? What are the prerequisites of the book? And in between Rotman's Advanced modern algebra and Grillet's Abstract Algebra which is good?
My background: I only had studied group theory yet ( up to permutation groups and little bit normal groups, iso(homo) morphisms) Thank you