Review of rings, division rings, prime and maximal ideals in a ring, nil radical, rings of quotients of domains, ID's, PID's, UFD's, the Wedderburn- Artin theorem, Hilbert basis theorem, polynomial rings, irreducible polynomials, Eisenstein criterion, algebraic extension of fields, algebraically closed fields, splitting fields, normal and separable extensions, finite fields, fixed fields. (3 credit hours).
