Math 721
Spring 2001
Exam 1
- Let
be projective 
modules. Show that 
is also a
projective 
module.
- Let
be an 
module. We define the dual module of 
to be: 
Assume that 
is a field and 
is a finite-dimensional vector space over 
Show that 
- Let
be an 
module and let 
be a free 
module on the set 
Show that 
- (Adjoint
associativity) Let
be commutative
with identity, and let 
be 
modules. Show that 
as 
modules.
- Let
be commutative
with identity,
ideals, and 
an 
module.
a)
Show that 
.
b)
Show that 
.
c)
Compute 
.