  We refine a well-known theorem of Auslander and Reiten about the extension
closedness of n-th syzygies over noether algebras. Applying it, we obtain the
converse of a celebrated theorem of Evans and Griffith on Serre's condition
(S_n) and the local Gorensteiness of a commutative ring in height less than n.
This especially extends a recent result of Araya and Iima concerning a
Cohen-Macaulay local ring with canonical module to an arbitrary local ring.
