Let R be a commutative ring with a unit and M an R-module. In this paper we give a comparison between the F-closure in M of an R-submodule having a minimal extension and the closure of this minimal extension for the same Gabriel topology defined on the ring R. If J(R) \in F we prove that both closures are the same. Moreover, if R is Artinian or semi-simple then the converse also holds.
Jacobson radical and closure of minimal extensions
HAJOUI, M. EL and MIRI, A. (2007) "Closure of Minimal Extensions," Turkish Journal of Mathematics: Vol. 31: No. 4, Article 7. Available at: https://journals.tubitak.gov.tr/math/vol31/iss4/7