A ring is said to be a right (left) hereditary ring if all of its right (left) ideals are projective as modules over . If is both left and right hereditary, then is simply called a hereditary ring.
Even though the notions of left and right heredity in rings are symmetrical, one does not imply the other.
If is semisimple, then is hereditary.
If is hereditary, then every free -module is a hereditary module.
The global dimension of a non-semisimple hereditary ring is 1.
|Date of creation||2013-03-22 14:48:50|
|Last modified on||2013-03-22 14:48:50|
|Last modified by||CWoo (3771)|