I am studying ring theory in this semester. I am new to this theory. Hence, I would like to have some recommendations on what books should be used for ring theory(beginner). If possible, I would like to have a book on theory and a lot of problems( include solution would be nicer,if possible). Can anyone give some recommendations?
Yu.Drozd, V.Kirichenko, Finite Dimensional Algebras (for 1st reading)
J.Lambek, Lectures on Rings and Modules (for 2nd reading)
I.Herstein, Noncommutative Rings (most preferable for me, but without exercises)
M.Atiyah, I.McDonald, Introduction to Commutative Algebra (if you will study algebraic geometry in the future)