Bass number

In mathematics, the "i"th Bass number of a module "M" over a local ring "R" with residue field "k" is the "k"-dimension of formula_1. More generally the Bass number formula_2 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 .
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 "i"th term of a minimal resolution of "M" is the Bass number formula_2.