Answer to Question #16726 in Abstract Algebra for john.george.milnor

Question #16726

Let R be a finite ring. Show that there exists an infinite sequence n1 < n2 < n3 < • • • of natural numbers such that, for any x ∈ R, we have x^n1 = x^n2 = x^n3 = • • • .

Expert's answer

Download Answer

Learn more about our help with Assignments: Abstract Algebra

Comments

No comments. Be the first!

Leave a comment

Related Questions

1. Let E = End(M) be the ring of endomorphisms of an R-module M, and let nM denote the direct sum of n
2. Is left artinian domain must be a division ring?
3. Let R be a domain. If R has a minimal left ideal, show that R is a division ring.
4. For any ring k, let A subspace of M(2,k) where a11+a21=a12+a22. Show that A is a subring of M2(k),
5. Let A be an algebra over a field k such that every element of A is algebraic over k. Let B be a suba
6. Let A be an algebra over a field k such that every element of A is algebraic over k. Show that a non
7. Let A be an algebraic algebra over a field k. Show that A is Dedekind-finite.

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…