I highly recommend learning abstract algebra thoroughly if you haven't already, by the way. It's a lot more well connected and well researched than you might think after just reading about this or that definition (groups, rings, quotient rings, lattice of ideals) in a vacuum. The magic comes when you mix all the definitions together. If you learn it correctly and master both the rigour and intuition behind it all, you'll come to consider your pre-abstract-algebra-self in the same Platonic cave as you might see your pre-linear-algebra-self right now.