Answer to Question #17355 in Abstract Algebra for sanches

Question

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”?

Answer 1

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.