Direct Summands of Syzygy Modules of the Residue Class Field

Abstract LetRbe a commutative Noetherian local ring. This paper deals with the problem asking whetherRis Gorenstein if thenth syzygy module of the residue class field ofRhas a non-trivial direct summand of finite G-dimension for somen. It is proved that ifnis at most two then it is true, and moreover, the structure of the ringRis determined essentially uniquely.