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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