Re: group -

From: JEMebius (jemebius_at_xs4all.nl)
Date: 11/20/04 

Date: Sat, 20 Nov 2004 17:29:12 +0100

Construct a homomorphism of the integer polynomials onto the integers as
follows:

Map 1, 2, 3, 4, ... onto 2, 4, 8, 16 ...
Map x, 2x, 3x, ... onto 3, 9, 27 ...
Map xx, 2xx, 3xx, ... onto 5, 25, 125, ...
etc., etc.,
and extend in the obvious way to sums and opposites of these monomials.
Use the unique factorization property of integers to prove that you
actually constructed an isomorphism.

Johan E. Mebius

Branch wrote:

>Let G be the additive group of all polynomials in x with interger
>coefficients.
>Show that G is isomorphic to the group Q* of all positive rationals
>under multiplication.
>
>Thanks!!
>
>