Math 724
Fall 2001
Homework 1
Due
September 17, 2001.
a)
Show
the radical of is itself an ideal.
b)
Show
that .
c)
Use
the previous parts to characterize the set of nilpotent elements of
Show that:
a)
If
is onto and
and
are one to one, then
is one to one.
b)
If
is one to one and
and
are onto, then
is onto
c)
Show
that this result has the short-five lemma as a corollary.