Auslander-Reiten and Huneke-Wiegand conjectures over quasi-fiber product rings

. In this paper we explore consequences of the vanishing of Ext for finitely generated modules over a quasi-fiber product ring R ; that is, R is a local ring such that R/ ( x ) is a non-trivial fiber product ring, for some regular sequence x of R . Equivalently, the maximal ideal of R/ ( x ) decomposes as a direct sum of two nonzero ideals. Gorenstein quasi-fiber product rings are AB-rings and are Ext-bounded. We show in Theorem 3.31 that quasi-fiber product rings satisfy a sharpened form of the Auslander-Reiten Conjecture. We also make some observations related to the Huneke-Wiegand conjecture for quasi-fiber product rings.