Date: Feb 3, 2013 11:25 PM
Author: magidin@math.berkeley.edu
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?

>

> Ask-an-Algebraist

>

>

>

> 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.

--

Arturo Magidin