example of reduced modules

example of reduced modules [closed]

Hi, All! Let's consider definition of REDUCED MODULES and TORSION MODULES:

A reduced module C is defined by the property that $Hom (A, C ) = 0$ for every divisible module A.

A left module A will be called a torsion module if $Hom (A, C) = 0$ for every torsion-free module C.

I can not find any example about reduced module and torsion module in this sense.

Please help me find some. I really appreciate your ideas!

edited Feb 24 2012 at 15:11

Martin Brandenburg
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asked Feb 24 2012 at 15:02

Student
1

$A = \mathbb{Z}_{n}$ is torsion and $C = \mathbb{Z}$ is tosion free. What can you say about $Hom(A,C)$ in this case? With the same $C$ and $A = \mathbb{Q}$, a divisible abelian group, what can you say about $Hom(A,C)$? – Chris Leary Feb 24 2012 at 16:26

closed as too localized by Andreas Blass, Martin Brandenburg, Bruce Westbury, Angelo, Sándor Kovács Feb 25 2012 at 1:48

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