Fulton 2.7
Posted on November 15, 20172.38.* Show that if and each
is finite dimensional over
then
Let be rings,
finite basis for
over
Then
is clearly a linearly independent spanning set for
Thus
The result then follows by induction.
2.39.* Prove the following relations among ideals in a ring
:
(a)
Suppose Then
Suppose
Then
and thus
So
(b)
Observe that where
Thus