Commutative Algebra - Paul Nelson - 2018

Charlotte, 23.01. 8:00-8:30

1. A commutative ring, x in A st for all primes P there is some n st x^n is in P. What can you say about x?

2. The following questions from the problem sheet: 3. 9. and 7.

Andreas, 23.01. 11:00-11:30

We started with a little bit of small talk about the exercises in general and moved to the same question as stated above: A commutative ring, x in A st for all primes P there is some n st x^n is in P. What can you say about x? The solution is that x is nilpotent, use that the intersection of all primes is the nilradical. Then he asked me how to prove this and I started to give the proof from the first chapter in Atiyah-MacDonald. He interrupted me quite fast, after I established the setting and asked for a different proof using localization. But here I was not sure and finished the proof of A-M orally. Then we discussed about the exercises 3,9 and 7 from the list, Good luck!