Unformatted text preview: Let R be an integral domain and let S be a subring of R which is a PID. Let Q be an injective Rmodule. Prove that Q is also an injective Smodule. Note that R and S have the same 1 (or maybe we assume this). Since Q is an injective Rmodule, we see that rQ = Q for all r ∈ R \ 0, in particular sQ = Q for all s ∈ S \ 0. It follows that Q is an injective Smodule, because S is a PID....
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 Fall '07
 PALinnell
 Math, Algebra, Ring, Ring theory, Commutative ring, injective left Rmodule

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