Answer to Question #23255 in Abstract Algebra for Hym@n B@ss

Question #23255

Show that in a right artinian ring R, every prime ideal p is maximal.

Expert's answer

R/p is semiprime and right artinian, so it issemisimple. Since R/p is in fact prime, it can have only one simplecomponent. Therefore, R/p is simple, so p is a maximal ideal.

Learn more about our help with Assignments: Abstract Algebra

Comments

No comments. Be the first!

Leave a comment

Related Questions

1. Show that a ring R is a domain iff R is prime and reduced
2. Let p ⊂ R be a prime ideal, A be a left ideal and B be a right ideal. Does AB ⊆ p imply that A �
3. For any semiprime ring R, show that Z(R) is reduced, and that char R is either 0 or a square-free in
4. Show that the center Z(R) of prime ring R is an integral domain, and char R is either 0 or a prime n
5. Show that a nonzero central element of a prime ring R is not a zero-divisor in R.
6. find a function just in 2 point has limit and prove it. and in the other hand find a function in n(i
7. a triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segment BD and DC into

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…