Answer to Question #24901 in Abstract Algebra for jeremy

Question #24901

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

Expert's answer

Not answered

Comments

No comments. Be first!

Leave a comment

Ask Your question

Related Questions

1.For a ring R, prove that: if every ideal of R is semiprime, then every ideal I of R is idempotent.
2.Let R be a k-algebra where k is a field. Let K/k be a separable algebraic field extension. Show that
3.Let R be a k-algebra where k is a field. Let K/k be a separable algebraic field extension. Show that
4.Let R,K be algebras over a commutative ring k such that R is k projective and K &supe; k. Show
5.If R &sube; Z(S), show that R ∩ Nil*(S) = Nil*(R).
6.Let R &sube; S be rings. Show that R ∩ Nil*(S) &sube; Nil*(R).
7.Show that Nil*R is precisely the set of all strongly nilpotent elements of R.