Let $K\subset E\subset\bar{K}$ be field extensions, $\bar{K}$ an algebraic closure of $K$. Denote $E_s$ the field of separable elements of $E$ over $K$, denote $\tilde{E}\subset\bar{K}$ the normal closure of $E/K$ (the minimal subfield of $\bar{K}$ which contains $E$ and is normal over $K$). Is i...

After having a solid year long undergraduate course in abstract algebra, I'm interested in learning algebra at a more advanced level, especially in the context of category theory. I've done some research, and from what I've read, it seems that using Lang as a main text and Hungerford as a supple...