Looking for advice on non_commutative ring theory: what is the successor subject, and textbook-recommendation?

Question

I plan to study non-commutative ring theory this semester, and here are two questions:

1. What is the successor subject of non-commutative ring theory, like algebraic number theory and algebraic geometry is "after" commutative algebra? Here non-commutative ring theory means what is covered, for example, by Rings and Categories of Modules, Kent R. Fuller (GTM 13) and A First Course in Noncommutative Rings, Lam (GTM 131).

2. What textbook do you recommend for non-commutative ring theory? How do you like Rings and Categories of Modules, Kent R. Fuller (GTM 13) and A First Course in Noncommutative Rings, Lam (GTM 131)? Are they good materials for students who want to self-study non-commutative ring theory?