Category Archives: Algebraic Geometry

What is an Infinitesimal?

A guest post from Reginald Anderson at Kansas State University. First-time learners of calculus often struggle with the notion of an infinitesimal, and considering $\frac{dy}{dx}$ literally as a fraction can lead students astray in Calculus III and differential equations, when … Continue reading

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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

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The “Idea” of a Scheme

The mathematical concept of a “scheme” seems to pop up everywhere, but it’s hard to get a good grasp on what a scheme actually is. Any time you might ask someone what a scheme is in passing, there never seems … Continue reading

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