Cotilting invariance of the Auslander-Reiten conjecture

Abstract

Let R be an associative ring with identity, and let T be a tilting right R-module, with S=End(T). It is known that if R is a Noetherian algebra that satisfies the Auslander-Reiten conjecture, then so is S. In this paper, we consider the dual situation where C is a cotilting right R-module, with S=End(C). We investigate the invariance of the property of satisfying the Auslander-Reiten conjecture when passing from R to S.

The article appears in the Journal of the Mathematical Society of Japan