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Answer to Question #17355 in Abstract Algebra for sanches

Question #17355
Let Ai (i ∈ I) be ideals in a ring R, and let A =(intersection on i) Ai. True or False: “If each R/Ai is J-semisimple, then so is R/A”?
Expert's answer
For each i, the J-semisimplicity of R/Ai implies that Ai is an intersection of maximal left ideals of R. Therefore, so is A =(intersection) Ai. This shows the J-semisimplicity of R/A. So it is True.

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