Date: Feb 3, 2013 10:21 PM Author: William Elliot Subject: Finite Rings > 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?

Ask-an-Algebraist

No - the trivial ring.

So add the premise that R has a nonzero element.