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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