@article{oai:soar-ir.repo.nii.ac.jp:00011873, author = {Takahashi, Ryo and Yassemi, Siamak and Yoshino, Yuji}, issue = {7}, journal = {PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY}, month = {Jul}, note = {Let R be a commutative Noetherian local ring. We show that R is Gorenstein if and only if every finitely generated R-module can be embedded in a finitely generated R-module of finite projective dimension. This extends a result of Auslander and Bridger to rings of higher Krull dimension, and it also improves a result due to Foxby where the ring is assumed to be Cohen-Macaulay., Let R be a commutative Noetherian local ring. We show that R is Gorenstein if and only if every finitely generated R-module can be embedded in a finitely generated R-module of finite projective dimension. This extends a result of Auslander and Bridger to rings of higher Krull dimension, and it also improves a result due to Foxby where the ring is assumed to be Cohen-Macaulay., Article, PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. 138(7):2265-2268 (2010)}, pages = {2265--2268}, title = {ON THE EXISTENCE OF EMBEDDINGS INTO MODULES OF FINITE HOMOLOGICAL DIMENSIONS}, volume = {138}, year = {2010} }