Simon will cover the basic definitions of groups, rings, homomorphisms, and ideals.
Rankeya will cover the following:
1) Zorn's Lemma and use it to prove important results such as the existence of maximal ideals in non-zero rings.
2) Define the radical of an ideal and prove that the radical of an ideal A of a ring R is the intersection of all prime ideals of R containing A, and then proceed to define the Nilradical and the Jacobson radical of a ring.
3) Discuss the prime spectrum of a ring if time permits.