Answer to Question #23256 in Abstract Algebra for Melvin Henriksen

Question #23256

Show that R is prime ring iff it is simple.

1

Expert's answer

2013-01-31T08:25:09-0500

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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