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> Let $R$ be a non-trivial ring with unity. We say $R$ is a **local ring** if there exists a unique maximal left-ideal.
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Let $R$ be a local ring. Then, how do I prove that there exists a unique maximal right-ideal?

I know that the maximal left-ideal is the Jacobson radical and it is the intersection of all the maximal right-ideals. However, I am not sure if this helps to prove the problem.