Date: Feb 4, 2013 12:55 PM
Subject: Re: Finite Rings
Arturo Magidin wrote:
>> >> x^2 = x, y^2 = x, z^2 = x
>> No -- you misread some of my specified conditions.
>> Look more carefully at how I defined the products
>> x^2, y^2, z^2.
>Quite right; sorry about that.
>But now note:
>x(yy) = xx = x; but (xy)y = 0y = 0.
>So you don't have an associative ring.
It never occurred to me that I'd lost associativity.
That pretty much destroys my attempted counterexample.
Thanks for the identifying the issue.