Date: Feb 3, 2013 11:25 PM
Subject: Re: Finite Rings
On Sunday, February 3, 2013 9:21:19 PM UTC-6, William Elliot wrote:
> > If R is a finite commutative ring without multiplicative identity
> > and if every element is a zero divisor, then does there exist
> > a nonzero element which annihilates all elements of the ring?
> No - the trivial ring.
Incorrect. The trivial ring *does* have a multiplicative identity. I'll let you figure out what it is and why it *does* satisfy the condition that 1x=x=x1 for all x in the ring.
In fact, I'll give you three guesses.
The first two don't count, though.
> So add the premise that R has a nonzero element.
Or, perhaps, not.