# Answer to Question #17353 in Abstract Algebra for sanches

Question #17353

If an ideal I ⊆ R is such that R/I is J-semisimple, show that I ⊇ rad R.

Expert's answer

The

*J*-semisimplicity of*R/I*means that the intersection of the maximal left ideals of*R*containing*I*is exactly*I*. It follows that rad*R*, the intersection of all the maximal left ideals of*R*, is contained in*I*.
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