On Gorenstein rings (Q1096701)

If R is noetherian, injective resolvents can be constructed. In this paper, it is shown that every injective resolvent \(...\to E_ 1\to E_ 0\to M\to 0\) is exact at \(E_ i\), \(i\geq n-1\), if and only if R is Gorenstein of dimension at most n. Additional characterizations of such rings are discussed. Finally, syzygies for injective resolvents are characterized in the case R is Gorenstein of dimension at most 1.