Math 726

Fall 2002

Homework 3

Due Monday, November 4, 2002. Do not forget to mark your “favorite” problem.

1. Let and be an ascending chain of subsets of a set Compute

2. Let be any module. Show that where is the family of finitely-generated submodules of

3. Show that if is an additive, right exact functor that preserves sums (e.g. ), then preserves direct limits.

4. Let the ordinary integers and let Compute the adic completion of

5. Consider the ring with ideal Compute the adic completion of