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