The Jacobson radical of a ring is presented along with the related theory and certain properties. Quasi-invertibility is introduced with the focus of proving the symmetric property of the definition of the Jacobson radical. The Jacobson radical is further discussed in the context of Artinian rings and the Wedderburn-Artin Theorem is proven, providing a classification of left Artinian rings with a trivial Jacobson radical. The Jacobson Density Theorem is proven and an application of the Jacobson radical theory is demonstrated.
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