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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 I2 ⊆ I. Then R/I hasa nonzero ideal I/I2 of square zero. This means I2 is not asemiprime ideal, so assumption does not hold.

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