From: Robin Chapman <rjc@maths.ex.ac.uk>
Subject: Re: Tensor Product
Date: Fri, 24 Sep 1999 09:00:41 GMT
Newsgroups: sci.math

In article <Pine.OSF.3.96.990923173743.490B-100000@alpha2.csd.uwm.edu>,
  Peter Hinow <phinow@csd.uwm.edu> wrote:
> Hello world,
>
> can someody help me with the following problem:
> Let Z_{p^n} the ring of integers mod p^n (p a prime) and consider
> the following tensor product over Z
>
> 	Q \otimes \prod_{n \in N} Z_{p^n}
>
> I have to show, that this group is nontrivial. How can I show
> for instance that the element
>
> 	(1 \otimes (1,1,1,...) )
>
> is not zero? Thanks for all hints!

Show that for an abelian group A, the kernel of phi: A -> Q (x) A
defined by phi(a) = 1 (x) a, is the torsion subgroup of A.

--
Robin Chapman
 http://www.maths.ex.ac.uk/~rjc/rjc.html
  "They did not have proper palms at home in Exeter."
    Peter Carey, _Oscar and Lucinda_


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