In mathematics, the ith Bass number of a module M over a local ring R with residue field k is the k-dimension of ${\displaystyle \operatorname {Ext} _{R}^{i}(k,M)}$. More generally the Bass number ${\displaystyle \mu _{i}(p,M)}$ 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 ${\displaystyle \mu _{i}(p,M)}$