Title: On the vanishing of self extensions over Cohen-Macaulay local rings,
Abstract: The celebrated Auslander-Reiten Conjecture, on the vanishing of self
extensions of a module, is one of the long-standing conjectures in ring theory.
Although it is still open, there are several results in the literature that
establish the conjecture over Gorenstein rings under certain conditions. The
purpose of this article is to obtain extensions of such results over
Cohen-Macaulay local rings that admit canonical modules. In particular, our
main result recovers theorems of Araya, and Ono and Yoshino simultaneously.