Bass number

In mathematics, the ith Bass number of a module M over a local ring R with residue field k is the k-dimension of . More generally the Bass number of a module M over a ring R at a prime ideal p is the Bass number of the localization of M for the localization of R (with respect to the prime p). Bass numbers were introduced by Hyman Bass (1963,p.11).

The Bass numbers describe the minimal injective resolution of a finitely-generated module M over a Noetherian ring: for each prime ideal p there is a corresponding indecomposable injective module, and the number of times this occurs in the ith term of a minimal resolution of M is the Bass number .


  • Bass, Hyman (1963), "On the ubiquity of Gorenstein rings", Mathematische Zeitschrift, 82: 8–28, CiteSeerX, doi:10.1007/BF01112819, ISSN 0025-5874, MR 0153708
  • Helm, David; Miller, Ezra (2003), "Bass numbers of semigroup-graded local cohomology", Pacific Journal of Mathematics, 209 (1): 41–66, arXiv:math/0010003, doi:10.2140/pjm.2003.209.41, MR 1973933
  • Bruns, Winfried; Herzog, Jürgen (1993), Cohen-Macaulay rings, Cambridge Studies in Advanced Mathematics, 39, Cambridge University Press, ISBN 978-0-521-41068-7, MR 1251956
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.