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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