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is Z injective

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The factor group Q/

**Z**and the circle group are also**injective Z**-modules. The factor group**Z**/nZ for n > 1 is**injective**as a**Z**/nZ-module, but not**injective**as an abelian group.Apr 14, 2017

1 answerI am trying to understand why Q is an injective abelian group but Z is not.
We say that an abelian group A is injective if it has the following property: ...

How to prove that Q is an injective Z-module via this definition?

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Injective ℤ-modules / abelian groups — An injective module over R is an injective object in RMod. This is the ...

and its quotient module Q/Z are examples of injective Z -modules. A direct product of injective modules is always ...

2 answers

Forgive me for this naive question.
We consider the following lemma and its proof in Lang's algebra, Third Ed., published 1999, Chap. 20, section ...

by RN Campbell(3) Every Abelian group is a Z-module, defined by 0g = 0, ng = g + ··· + g (n times) , and. (−n)g = n(−g) for g ∈ G and for ... 2015 Cited by 2 —