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 .