Modules without Self-Extensions over Radical Cube Zero Rings Original Research Article

A conjecture of Tachikawa states that every finitely generated non-projective module M over a self-injective artinian ring R has a self-extension, i.e., ExtiR(M, M) ≠ 0 for some i ≥ 1. We show that Tachikawa′s conjecture holds for a class of radical cube zero rings.