My problem is: If the sum of to non-units in a ring $R$ is non-unit, then the Jacobson radical $J(R)$ is maximal. I need help please. I have no idea how to start. I thought that if the set of all non-units is an ideal of $R$, then it turns to be the unique maximal left ideal of $R$ and so it is $J(R)$.
2026-03-25 12:28:10.1774441690
The sum of two non-units of a ring $R$ is a non-unit implies that the Jacobson radical is maximal.
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