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Tag Archives: Math
Introduction to Ideal Class Groups
Algebraic number theory is a really interesting subject, but unlike some other subjects, it’s not 100% clear what objects people study. This post provides an introduction to the class group of a finite dimensional field extension of $\mathbb{Q}$, an object often … Continue reading
Intersection of a Chain of Subsets
Assume $\{F_x\}_{x \in \Gamma}$ is a collection of subsets (of a notso important set!) such that every two are comparable, i.e for any $x$ and $y$, either $F_x \subset F_y \ \ $ or $\ \ F_x \supset F_y \ … Continue reading
MachineChecked Proof
“In my view, the choice between the conventional process by a human referee and computer verification is as evident as the choice between a sundial and an atomic clock in science.” – Tom Hales (from [4]) “The rapid advance of … Continue reading
Gauge Theory and LowDimensional Topology (Part II: Smooth FourManifolds)
In the last post, I attempted to give an overview of the state of affairs in fourmanifold topology leading up to the introduction of gauge theory. In particular, we discussed the correspondence between (topological) fourmanifolds and their intersection forms afforded by … Continue reading
A Pretty Lemma About Prime Ideals and Products of Ideals
I was trying to prove a theorem in algebraic geometry which basically held if and only if this lemma held. Here’s the lemma: Lemma: Given any ring $A$, a prime ideal $ \mathfrak{p} \subset A$, and a finite collection of ideals … Continue reading