ON THE EXISTENCE OF EMBEDDINGS INTO MODULES OF FINITE HOMOLOGICAL DIMENSIONS

• Takahashi, Ryo

• Yassemi, Siamak

• Yoshino, Yuji

抄録

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)

収録刊行物

• PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY

  PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY 138 (7), 2265-2268, 2010-07

  AMER MATHEMATICAL SOC

キーワード

• Gorenstein ring
• Cohen-Macaulay ring
• projective dimension
• injective dimension
• (semi)dualizing module

詳細情報

• CRID: 1050001338921986688
• NII論文ID: 120007114208
• NII書誌ID: AA00781790
• ISSN: 00029939
• HANDLE: 10091/10837
• Web Site: https://soar-ir.repo.nii.ac.jp/records/11873
• 本文言語コード: en
• 資料種別: journal article
• データソース種別:
  • IRDB
  • CiNii Articles