If R had been unitary I would've solved it by now (thanks to Hacker).

I know how to prove R has no zero divisors if R is unitary...

But I'm positive it's not a given, and cannot find a counter-example as you suggested.

Mind you giving me that counter example?

Funny, a friend of mine told me yesterday he has proved R must have a unit but didn't mention how (I didn't work on it yesteday and didn't want him to "spoil" all the fun...

). Now he's asleep so I cannot contact him anyhow :-\

and THANK YOU.