Answer to Question #22740 in Abstract Algebra for Mohammad

Abstract Algebra

Question #22740

Let R be any ring whose additive group is torsion-free. Show (without using Amitsur’s Theorem) that J = rad R[t] <> 0 implies that R ∩ J <> 0.

Expert's answer

Answer in progress...

Learn more about our help with Assignments: Abstract Algebra

Comments

No comments. Be the first!

Leave a comment

Related Questions

1. Give an example of a ring R with rad R is nonzero but rad R[t] = 0.
2. Given an element a in a commutative ring R, let S be the multiplicative set 1 + aR ⊆ R. Does a ∈
3. Given an element a in a commutative ring R, let S be the multiplicative set 1 + aR ⊆ R. Show that
4. Let R be a commutative domain and S^(−1)R be the localization of R at a multiplicative set S. Is
5. Let R be a commutative domain and S^(−1)R be the localization of R at a multiplicative set S. Is
6. Let R be a commutative domain and S^(−1)R be the localization of R at a multiplicative set S. Is
7. Is true statement over arbitrary ring: "If R is a commutative ring or a left noetherian ring, t