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I am asked to provide an example of a ring $(R,+,\cdot)$ and a Abel group $(M,+)$ such that when $\cdot$ is provided for $M$, an $R$-module can not be formed.

A bit strange question considering, that the definition of a module says that the ring must be unit-ring, such that $0_R\neq 1_R$. So if I construct such a ring, an $R$-module can not be formed.

However, perhaps that's not the intention here, in which case, how could I construct an example provided the ring satisfies the conditions?

Tony
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1 Answers1

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Let $R=\mathbb Z/2\mathbb Z$ and $M=\mathbb Z$. What are the possible homomorphisms $\mathbb Z/2 \mathbb Z \to \mathrm{End}(\mathbb Z) \cong \mathbb Z$?

Andres Mejia
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