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