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    Rings : Von Neumann Regularity and Jacobson Radicals

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    An element a of a ring R with unity is von Neumann regular if there exists b such that aba = a. Show that the only element in Jacobson radical J[R] having this property is the zero element.

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    Solution Summary

    Von Neumann Regularity and Jacobson Radicals are investigated. The solution is detailed and well presented.