Stage 4 Algebra

Materials mentioned in stage 3, which have not been covered there, can be studied at this stage, for example, Artin, Dummit and Foote.

My lecturer Daniel Chan's web page contains lots of algebra stuffs.

In general:

Advanced Linear Algebra:

Groups and Lie Algebras:

Rings, Fields and Galois Theory:
Note several stage 3 algebra texts also introduce Galois Theory. For example, J.B. Fraleigh's one.

Modules and Representation Theory:

Commutative Algebra:

Homological Algebra and Category: