Answer to Question #19032 in Abstract Algebra for Hym@n B@ss

Question #19032

Show that the following conditions on a ring R are equivalent:
(1) All ideals not equal R are prime.
(2) (a) The ideals of R are linearly ordered by inclusion, and (b) All ideals I ⊆ R are idempotent.

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. For any given division ring k, list all the prime and semiprime ideals in the ring R of 3 × 3 upper
2. Show that R is prime ring iff it is simple.
3. Show that in a right artinian ring R, every prime ideal p is maximal.
4. Show that a ring R is a domain iff R is prime and reduced.
5. Let p ⊂ R be a prime ideal, A be a left ideal and B be a right ideal. Does AB ⊆ p imply that A �
6. For any semiprime ring R, show that Z(R) is reduced, and that char R is either 0 or a square-free in
7. Show that the center Z(R) of prime ring R is an integral domain, and char R is either 0 or a prime n

Who Can Help Me with My Assignment

There are three certainties in this world: Death, Taxes and Homework Assignments. No matter where you study, and no matter…
How to Finish Assignments When You Can’t

Crunch time is coming, deadlines need to be met, essays need to be submitted, and tests should be studied for.…
How to Effectively Study for a Math Test

Numbers and figures are an essential part of our world, necessary for almost everything we do every day. As important…