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