Math 720
Fall 2000
Final Exam
a)
Show that is a metric on the set
and
b)
Show that is a dense subspace
of
c)
Describe the unit circle in and
Show that if
is a field, then the unit circle in R[[x]] is also a
group.
d) Show in general that the units of R[x] and the units of R[[x]] are not isomorphic.
with
Show that