MODULES OF QUOTIENTS OVER COMMUTATIVE RINGS

In [3] Goldman introduced the notion of modules of quotients of a ring with respect to an idempotents kernel functor, which is a generalization of the localization of a module with respect to a multiplicative subset of a communtative ring. For an idempotent kernel functor $\sigma$ on the category of R-modules and for an R-module M, let $Q_\sigma(M)$ denote the module of quotients with respect to $\sigma$.