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Question Number 75954 by mhmd last updated on 21/Dec/19
prove that (ann(I),+,.) identical in (R,+,.)?
$${prove}\:{that}\:\left({ann}\left({I}\right),+,.\right)\:{identical}\:{in}\:\left({R},+,.\right)? \\ $$
Commented by kaivan.ahmadi last updated on 21/Dec/19
its a right ideal no identical
$${its}\:{a}\:{right}\:{ideal}\:{no}\:{identical} \\ $$
Commented by kaivan.ahmadi last updated on 21/Dec/19
x∈annI⇒xI=0  if r∈R⇒rxI=0⇒rx∈annI  ⇒I is an right ideal.
$${x}\in{annI}\Rightarrow{xI}=\mathrm{0} \\ $$$${if}\:{r}\in{R}\Rightarrow{rxI}=\mathrm{0}\Rightarrow{rx}\in{annI} \\ $$$$\Rightarrow{I}\:{is}\:{an}\:{right}\:{ideal}. \\ $$$$ \\ $$$$ \\ $$

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