Math 724
Fall 2001
Exam 1
You
may use any text and me. Due Friday October 19, 2001.
a)
Show
that
b)
(Lamentations)
In this part we show that part a) almost never works for power series. Show
that if is a UFD and is a multiplicatively closed subset of then but equality holds if
and only if (and so the
localization is superfluous).
c)
Give
an example of a ring and an ideal such that is strictly contained
in the ideal (This is contrary to
the polynomial situation where ).