Re: Exact sequence
- From: magidin@xxxxxxxxxxxxxxxxx (Arturo Magidin)
- Date: Fri, 10 Feb 2006 14:35:43 +0000 (UTC)
In article <1139545210.466432.194000@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
<mskirvin@xxxxxxxxx> wrote:
Gmath wrote:
Is it true that there exists a short exact sequence of abelian group 0
---> Z_9 -----> Z_27 + Z_3 -----> Z_9 -----> 0 where Z_n is a set of
interger modulo n and + denote the direct sum.?? If it exists , what
are the maps from Z_9 to Z_27 + Z_3 and Z_27 + Z_3 to Z_9? Thank you
for any helps.
No, such an exact sequence cannot exist. Z_9 injects into (Z_27 + Z_3)
as (Z_9 + 0).
And yet, that is not the only way it injects. It also embedds by
mapping [1] to ([3],[1]). What is the quotient of Z_27 + Z_3 modulo
<([3],[1])>?
[.rest deleted.]
--
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Arturo Magidin
magidin@xxxxxxxxxxxxxxxxx
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