91Ó°ÊÓ

Show that any primitive ring is prime. Conversely, if \(R\) is a prime ring with a minimal right ideal, prove that \(R\) is primitive. Give an example of a prime ring that is not primitive.

Prove that a prime Artinian ring is simple. Give an example of a primitive ring that is not simple. For this, let \(V\) be an infinite dimensional \(K\)-vector space and let \(R\) be a suitable subring of End \(_{K}(V)\).