Ring without zero divisors
- From: Ben <benv@xxxxxxxx>
- Date: 1 May 2007 12:07:22 -0700
I have following question.
Is it true, that if we have a ring R (with unit) without zero divisors
(*) for all x there is y such that yx^3y = x,
then R is divison ring?
I can write these observations
- Two sided ideals of R are idempotent (I^2=I)
- The elements y and x^4 (as above) commute, because x^4y = xx^3y =
yx^3yx^3y = yx^3 x = yx^4.
Thank you for your ideas how to prove this or for your counterexamples!