# Answer to Question #17274 in Algebra for sanches

Question #17274

Show that any maximal ideal I of R is the annihilator of some simple left R-module, but not conversely.

Expert's answer

Let

*V*=*R/*m, where mis a maximal left ideal of*R*containing*I*. Then*IV*= 0, so*I**⊆**ann(**V*). Since ann(*V*) is an ideal of*R*, themaximality of*I*implies that*I*= ann(*V*).
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