Direct summands of syzygy modules of the residue class field

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/125232Let R be a commutative Noetherian local ring. This paper deals with the problem asking whether R is Gorenstein if the n-th syzygy of the residue field of R has a nontrivial direct summand of finite G-dimension for some n. It is proved that if n is at most two then it is true, and moreover, the structure of the ring R is determined essentially uniquely.18 pages, to appear in Nagoya Mathematical JournalCommutative Algebra13D02 (Primary) 13D05, 13H10 (Secondary)Direct summands of syzygy modules of the residue class fieldtext