충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제34권4호
  • /
  • Pages.335-343
  • /
  • 2021
  • /
  • 1226-3524(pISSN)
  • /
  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

VARIOUS REMARKS ON HOMOLOGICAL INVARIANTS OF LOCAL RINGS

  • Lee, Kisuk (Department of Mathematics Sookmyung Women's University)
  • 투고 : 2021.11.04
  • 심사 : 2021.11.25
  • 발행 : 2021.11.15
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this article, we investigate the finiteness of Auslander Index when a ring A has not necessarily a canonical module, or a Gorenstein module. We also study the relations between column invariants and row invariants.

키워드

참고문헌

  1. W. Bruns and J. Herzog, Cohen-Macaulay rings, Camb. Stud. Adv. Math., 39 Cambridge Univ. Press, Cambridge (1993)
  2. S. Ding, Cohen-Macaulay approximations and multiplicities, J. Alg., 153 (1992), 172-188. https://doi.org/10.1016/0021-8693(92)90156-G
  3. S. Ding, A note on the index of Cohen-Macaulay local rings, Comm. Alg., 21 (1993), 53-71. https://doi.org/10.1080/00927879208824550
  4. D. Eisenbud, Homological algebra on a complete intersection with an application to group representations, Trans. Amer. Math. Soc., 260 (1980), 35-64. https://doi.org/10.1090/S0002-9947-1980-0570778-7
  5. J. Koh and K. Lee, Some restrictions on the maps in the minimal resolutions, J. Alg., 202 (1998), 671-689. https://doi.org/10.1006/jabr.1997.7310
  6. J. Koh and K. Lee, New invariants of Noetherian local rings, J. Alg., 235 (2001), 431-452. https://doi.org/10.1006/jabr.2000.8506
  7. J. Koh and K. Lee, On column invariant and index of Cohen-Macaulay local rings, J. Korean Math. Soc., 43 (2006) no. 4, 871-883. https://doi.org/10.4134/JKMS.2006.43.4.871
  8. K. Lee, Column invariants over Cohen-Macaulay local rings, Comm. Alg., 33 (2005) no. 5, 1303-1314. https://doi.org/10.1081/AGB-200060500
  9. K. Lee, Computation of numerical invariants col(-), row(-) for a ring k[[te, te+1, t(e-1)e-1]], J. Korea Math., 33 (2000), 521-530.
  10. K. Lee, Presenting matrices of maximal Cohen-Macaulay modules, Bull. Korean Math. Soc., 44 (2007), no. 4, 871-878. https://doi.org/10.4134/BKMS.2007.44.4.871
  11. G. Leuschke, Gorenstein modules, finite index, and finite Cohen-Macaulay type, Comm. Alg., 30 (2002), no. 4, 2023-2035. https://doi.org/10.1081/AGB-120013229