Date: Feb 4, 2013 12:55 PM
Author: quasi
Subject: Re: Finite Rings
Arturo Magidin wrote:

>quasi 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.

Ouch!

It never occurred to me that I'd lost associativity.

That pretty much destroys my attempted counterexample.

Oh well.

Thanks for the identifying the issue.

quasi