# 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/*A*i*implies that A*i*is an intersection of maximal left ideals of*R*. Therefore, so is A =(intersection) A*i*. This shows the*J*-semisimplicity of*R/*A. So it is True.
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