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comment Endomorphisms of a ring $R$ considered as $R$-module
@BrettFrankel Thanks. Looks like I was trying to make things much too complicated.
Apr
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comment Endomorphisms of a ring $R$ considered as $R$-module
So if $\varphi(1)=v$, then $\varphi(x)=vx$ for every $x\in V$. Then my answer is there is a homomorphism $\varphi_v$ that sends $x\leadsto xv$ for each $v\in V$. Is that right?