How can I prove that if a domain $R$ is an injective module, then $R$ is a field?

Asked Dec 05 '19 at 13:34

Active Dec 05 '19 at 13:58

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What are the similarities between a field and a projective module that can support my question?

edited Dec 05 '19 at 13:58

Kenta S

asked Dec 05 '19 at 13:34

Marcos Eusébio

4

I'm guessing you mean projective by objective, and field by body.
https://math.stackexchange.com/questions/93539/if-r-is-an-integral-domain-and-every-r-module-is-projective-must-r-be-a – take008 Dec 05 '19 at 13:37
In fact, I refer to the injection modules – Marcos Eusébio Dec 05 '19 at 14:06
https://math.stackexchange.com/questions/213275/injective-integral-domains-are-fields – take008 Dec 05 '19 at 14:42

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