The seventh chapter of Ragnar's celebrated manuscript is titled "Multiplicative Structure, Duality and Support". I will talk about the last section of this chapter: the support of Tate cohomology. I will give an overview of this section and talk about the work of Srikanth Iyengar and Ryo Takahashi on the cohomology annihilators. There will be two proofs of why Jacobian ideal of a hypersurface ring must be contained in the cohomology annihilator ideal. Then, I will look at the cohomology annihilator ideal of one dimensional Gorenstein rings and explain an observation of Ragnar. Finally, I will generalize the ideas from dimension one to higher dimensions.