Answer to Question #24903 in Abstract Algebra for jeremy
If R is commutative, then, every ideal of R is semiprime implies R is von Neumann regular.
Let a ∈ R. Then a2R is asemiprime ideal; that is, R/a2R is reduced. Thisimplies that a ∈ a2R, so we have that R is von Neumannregular.
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