Reading: Class notes. Eisenbud: Sections 3.1-3.3 through Proposition 3.9 (ideal case only), Corollary 2.12. Atiyah-MacDonald: Chapter 4 through Proposition 4.8.
Exercises: Eisenbud: 3.1, 3.14.
Exercise C: Prove that if R is a Noetherian ring, then so is R[[x1, ..., xn]].
Exercise D: Show that the associated primes of the ideal I = (x2, xy) in k[x,y] are precisely (x) = ann y and (x, y) = ann x.
Exercise E: Let p be a prime ideal of a ring R and n be a natural number. The R-ideal p(n) := R ∩ pn Rp is called the nth symbolic power of p. Show that p(n) is primary.Last modified: (2019-10-09 11:40:29 CDT)