example of a projective module which is not free
where on the right side we have the multiplication in a ring .
Proposition. Both and are projective -modules, but neither nor is free.
Assume now that is free, i.e. there exists which is a basis. Take any . Both and are nontrivial and thus in both and . Therefore in , but
|Title||example of a projective module which is not free|
|Date of creation||2013-03-22 18:49:55|
|Last modified on||2013-03-22 18:49:55|
|Last modified by||joking (16130)|