Herstein Commutivity ProblemDate: 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/ |
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