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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, soI ⊆ ann(V ). Since ann(V ) is an ideal of R, themaximality of I implies that I = ann(V ).

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