# Answer to Question #24902 in Abstract Algebra for jeremy

Question #24902

R is von Neumann regular, prove that: every ideal I of R is idempotent.

Expert's answer

Let

*I*be any ideal of*R*.For any*a**∈**I*, we have*a**∈**aRa**⊆**I*^{2}, so clearly*I*^{2}=*I*,and ideal*I*of*R*is idempotent.
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