# Answer to Question #24900 in Abstract Algebra for jeremy

Question #24900

For a ring R, prove that: if every ideal of R is semiprime, then every ideal I of R is idempotent.

Expert's answer

If conclusion does not hold, thereexists an ideal

*I*such that*I*2*⊆**I*. Then*R/I*hasa nonzero ideal*I/I*2 of square zero. This means*I*2 is not asemiprime ideal, so assumption does not hold.Need a fast expert's response?

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