Let $R$ be a non-trivial ring with unity. We say $R$ is a local ring if there exists a unique maximal left-ideal.
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.