Question
Let $a$ belong to a commutative ring $R$. Show that $a R=\{a r \mid r \in R\}$ is an ideal of $R$. If $R$ is the ring of even integers, list the elements of $4 R$.
Step 1
To do this, we need to show that $aR$ is a subgroup of $R$ under addition and that it is closed under multiplication by elements of $R$. Show more…
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