Let "S" and "R" be rings, and "P" be a left-"R", right-"S" bimodule that is flat as a left-"R" module. For any injective right "S"-module "M", the set of module homomorphisms Hom"S"( "P", "M" ) is an injective right "R"-module. For instance, if "R" is a subring of "S" such that "S" is a flat "R"-module, then every injective "S"-module is an injective "R"-module. In particular, if "R" is an integral domain and "S" its field of fractions, then every vector space over "S" is an injective "R"-module. Similarly, every injective "R"["x"]-module is an injective "R"-module.