Herstein Commutivity Problem

Date: 09/24/2002 at 15:31:46
From: Ben
Subject: Ring theory

Prove that if x = x^3 for all x in R (a ring), then R is commutative. 

I found this in _Topics in Algebra_ by Herstein. Any help would be 
greatly appreciated.

Date: 09/25/2002 at 13:07:42
From: Doctor Wilkinson
Subject: Re: Ring theory

This is a famous problem and quite difficult. Here's a site that has a
short and clever proof. You might want to try proving the Lemmas for
yourself before reading them. The first two are easy.

   Puzzles - Torsten Sillke
   http://www.mathematik.uni-bielefeld.de/~sillke/PUZZLES/herstein 

- Doctor Wilkinson, The Math Forum
  http://mathforum.org/dr.math/