Answer to Question #24900 in Abstract Algebra for jeremy
For a ring R, prove that: if every ideal of R is semiprime, then every ideal I of R is idempotent.
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.