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| Name | Commutative algebra 14 (Irreducible subsets of Spec R) |
| Video Uploader | Video From Richard E Borcherds |
| Upload Date | This Video Uploaded At 18-08-2020 21:16:18 |
| Video Discription | This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. In this lecture we show that the irreducible closed subsets of Spec R are just the closures of points. We do this using the lemma that if an ideal I is disjoint from a multiplicative subset S, then there is a prime ideal P containing I and disjoint from S. As another application of this lemma we discuss the maximal and prime ideals of the ring of continuous functions on a compact Hausdorff space, showing that it has some rather strange prime ideals. Correction: On sheet 4 at about 7:00 the reason why no power of a is in I should be that I is radical, not that I is prime (which is what we are trying to prove). Reading: Lectures 9-15 about visualizing rings do not correspond directly to sections of the textbook. Exercises: 1.9, 1.11, 1.25 [-WdBg_jL_ds] |
| Category | Education |
| Tags | Commutative algebra | Irreducible set | spectrum of a ring |
