# Answer to Question #24903 in Abstract Algebra for jeremy

Question #24903

If R is commutative, then, every ideal of R is semiprime implies R is von Neumann regular.

Expert's answer

Let

*a**∈**R*. Then*a*^{2}*R*is asemiprime ideal; that is,*R/a*^{2}*R*is reduced. Thisimplies that*a**∈**a*^{2}*R*, so we have that*R*is von Neumannregular.
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