module notation

**badgerigar** · May 16th 2009, 01:15 AM

Hi. I'm trying to figure out what $M=Rm$ means in an assignment question (I won't post the question since its being marked). Some possibly relevant context:
$M$ is an $R$ module
$R$ is a PID
$\textrm{ann}_R(m) = (p)$ for some $p \in R$

**NonCommAlg** · May 16th 2009, 01:06 PM

Originally Posted by badgerigar

Hi. I'm trying to figure out what $M=Rm$ means in an assignment question (I won't post the question since its being marked). Some possibly relevant context:

$M$ is an $R$ module.

it means $M,$ as $R$ module, is generated by $m \in M.$ in other words $M=Rm=\{rm: \ r \in R \}.$

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