Reading: Class notes. Atiyah-MacDonald: Chapter 4 from Proposition 4.7, Sections 7.11-7.17. Eisenbud: Theorem 3.10b (ideal case only), Section 3.8, Chapter 4 through Section 4.4.
Exercises: Eisenbud: 3.6, 3.7, 3.8 (Use suggested approaches to these problems at the end of the text), 4.7, 4.24.
Exercise F: Let R ⊂ S ⊂ T be rings. Show that if S is integral over R and T is integral over S, then T is integral over R. Deduce that the double normalization (integral closure) of R in T (first, normalize R in S and then take the normailzation in T of that normalization) is the same as the single one, the normalization of R in T.
Last modified: (2019-11-15 21:58:59 CST)