Invariant rings have interested mathematicians for centuries. In particular, when one considers finite groups, determining that the ring of invariants is finitely generated and finding a bound on the degree of a set of generators were problems addressed by Hilbert and Noether, respectively. In the case of Abelian groups, there is a conjecture for the bound that has been proven in some cases, but still remains open in the general case. We discuss this problem and present a possible approach to it. Speaker(s): Francesca Gandini (University of Michigan)