To do analysis on commutative rings, we need a metric, and to prove that the distance function we have is actually a metric, we need to show that it satisfies the three conditions for a metric. Two are easy to prove, but the third requires Krull's Intersection Theorem. Standard proofs of this theorem require advanced knowledge and complicated lemmas, but I'll explain a new, simpler proof that requires only abstract algebra.Above you will find the title and abstract for my colloquium on September 25 at 1 pm. The proof is not mine; I will merely be explaining it. Feel free to come.
2 days ago