Re: Prove that a set is a monoid, but not a ring

In article
<12255104.1114440699431.JavaMail.jakarta@xxxxxxxxxxxxxxxxxxxxxx>,
grimster <kelvarnsen1@xxxxxxxxxxx> wrote:

>ok, i did this as well. can anyone give me an example that shows that
>end n(k) is not a ring? an example that shows that distribuitivity
>fails...

To return lost context, you are trying to show that the polynomial
maps from k^n to k^n form a monoid under composition, but not a ring
(under, presumably, pointwise addition and composition).

So... Take n=1, let g(x) = x, h(x) = 1, and f(x) = x^2. You want to
show that f(g+h) is not equal to fg + fh. That should be trivial, at
least for k not of characteristic 2.

--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes")
======================================================================

Arturo Magidin
magidin@xxxxxxxxxxxxxxxxx

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