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.
It never occurred to me that I'd lost associativity.
That pretty much destroys my attempted counterexample.