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.
1
Expert's answer
2012-10-31T08:53:17-0400
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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