Abstract:

A generalized hereditary pretorsion class F are defined, that is the class of right R-module F is closed under pure submodule, direct limits, and pure homomorphism image. It is shown that if Fis a generalized hereditary pretorsion class closed under extension and R∈F, then every right R-module has an F-cover. And it is proved that if Fis a generalized hereditary pretorsion class, then every right R-module has an F-preenvelope if and only if F is closed under products.

Key words: F-cover; F-precover; F-preenvelope