My book is trying to show that the rngs ##2 \mathbb{Z}## and ##3 \mathbb{Z}## are not isomorphic. It starts by saying that if there were an isomorphism ##\mu : 2 \mathbb{Z} \to 3 \mathbb{Z}## then by group theory we would know that ##\mu (2) = \pm 3##. It then goes on to show that this leads to a contradiction. My question has to do with why it must be true, if we assume ##\mu## is an isomorphism, that ##\mu (2) = \pm 3##(adsbygoogle = window.adsbygoogle || []).push({});

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# I Isomorphism between 2Z and 3Z

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