Re: Agh, this ought to be easy... (linear algebra)

In article <44e1dc2e$3$fuzhry+tra$mr2ice@xxxxxxxxxxxxxxxx>,
Shmuel (Seymour J.) Metz <spamtrap@xxxxxxxxxxxxxxxxxxxxxxxxxx> wrote:
In <1155600324.071260.111620@xxxxxxxxxxxxxxxxxxxxxxxxxxx>, on
08/14/2006
at 05:05 PM, adomplayer@xxxxxxxxx said:

I am trying to show that if an nxn matrix M w/elements from ring R
with 1 is not a diagonal matrix, then it is not in the center of the
nxn matrix ring of R.

What happes if every element of R other than 1 is nilpotent?

Doesn't matter. As Lee said, you just look at the products MA
and AM where A is all 0's except for a single 1. In any ring
with 1, 1x = x1 = x and 0x = x0 = 0.

Robert Israel israel@xxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada

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