**Pure Math Grad Student Colloquium**

MC 5136B

Thursday, March 1

3:30 — 4:30 p.m.

Title: From algebraic Galois to differential Galois theory

Courtesy of Harmony. Not sure if I’ll go to this, what with the 450 and 764 assignments both due Friday (goodbye, sleep). “Differential Galois theory” has a bit of a fatal ring to it (beautifully fatal, but fatal nonetheless)…

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## About mlbaker

just another guy trying to make the diagrams commute.

Hope you are doing well in the assignments. 764’s is kind of difficult what about the 450’s?

450 is going quite well π I’ll probably finish it in about 2 hours or so, at which point I’ll be doing 764 until .

I am currently doing 764. Let me know if I can help in any way. I will be doing 764 for the same minimum as you π

Cool! π I have a feeling the “direct product of local rings” question will turn out rather elegant…

I do not know I am leaving this question to the end and solving the easy questions first to maximize my grade :).

Apparently, this question is equivalent to the primary decomposition theorem for Noetherian rings. Since R is finite dimensional. Then it is noetherian, and Since R is a k-algebra. the primary ideals will be local rings. Therefore, since a noetherian ring is the direct product of its primary parts. R will be a direct product of Local rings.

Primary decomposition theorem? I think that’s a bit above me…

Come on, you are amazing. You must know this. It is somehow a generalization of the prime factorization for rings