# Answer to Question #23256 in Abstract Algebra for Melvin Henriksen

Question #23256

Show that R is prime ring iff it is simple.

Expert's answer

*R*is prime ring then

*R/*p is semiprime andright artinian, so it is semisimple. Since

*R/*p is in fact prime, it canhave only one simple component. Therefore,

*R/*p is simple, then so does

*R*.

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