“…The rings of Theorems A and B have decomposable maximal ideals, which means that they are realized as non-trivial fiber products; see Fact 2.1 below. Such rings have very rigid homological properties, as one sees, e.g., in [5,16,17,21,23]. For instance, they satisfy (UAC), they have at most the two trivial semidualizing modules, they are G-regular, and they satisfy the Auslander-Reiten Conjecture.…”