Nathan Jacobson's Basic Algebra I, II covers many topics in Algebra that is probably even beyond many pure mathematics full professor's scope of knowledge, unless the professor is specialised in algebra.
My question is, if the following topics are included in Basic Algebra:
- Modules over a PID;
- Galois Theory;
- Algebras over a Field;
- Lattices and Boolean Algebras.
- Classical Representation Theory;
- Homological Algebra;
- Commutative Ideal Theory;
- Field Theory;
- Valuation Theory;
- Dedekind Domains.
Then what is considered (according to N. Jacobson's standard) as "Intermediate Algebra" and what is considered "Advanced Algebra"? Any list of topics and recommended textbooks on Intermediate Algebra and Advanced Algebra?