GF-Regular Modules

Abstract EN

We introduced and studied GF-regular modules as a generalization of π-regular rings to modules as well as regular modules (in the sense of Fieldhouse).

An R-module M is called GF-regular if for each x∈M  and r∈R, there exist t∈R and a positive integer n such that rntrnx=rnx.

The notion of G-pure submodules was introduced to generalize pure submodules and proved that an R-module M is GF-regular if and only if every submodule of M is G-pure iff M? is a GF-regular R?-module for each maximal ideal ? of R.

Many characterizations and properties of GF-regular modules were given.

An R-module M is GF-regular iff R/annx is a π-regular ring for each 0≠x∈M iff R/annM is a π-regular ring for finitely generated module M.

If M is a GF-regular module, then JM=0.