Self-injective commutative rings have no nontrivial rigid ideals

Abstract

We establish a link between trace modules and rigidity in modules over Noetherian rings. Using the theory of trace ideals we make partial progress on a question of Dao, and on the Auslander-Reiten conjecture over Artinian Gorenstein rings.

6 pages; corrected some typos

Cited by in corpus (1)

• When are the rings $I:I$ Gorenstein?