2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73913Let R be a commutative Noetherian local ring with residue class field k. In this paper, we mainly investigate direct summands of the syzygy modules of k. We prove that R is regular if and only if some syzygy module of k has a semidualizing summand. After that, we consider whether R is Gorenstein if and only if some syzygy module of k has a G-projective summand.13 pages, to appear in Journal of AlgebraCommutative Algebra13C13 (Primary) 13D02, 13D05, 13H05, 13H10 (Secondary)text