A Note on FMS Modules and FCP Extensions

Abstract

Let R be a commutative ring with unity and S be a (unital) subring of R such that R is integral over S and S⊆R has FCP. Let M be an R-module. For any submodule N of M, it is shown that R(+)N⊆R(+)M has FCP if and only if S(+)N⊆S(+)M has FCP. We also discuss FMS modules.