Re:대수입니다. 증명 좀 부탁드립니다. 아시는 분 좀 까다라운 문제라서 도저히 모르겠네요.

[비는아픔]

Let be an integral domain and be a ring homomorphism.

Then  so or .

If , trivially .

Now suppose and .

For any ( and is nonzero),

so , i.e., .

Finally assume that and .

For any nonnegative , .

This implies for any with , so is increasing.

Now noting that if as we’ve seen just before, suppose for some .

Since is dense in , there exists such that .

This contradicts the fact that is increasing.

On the other hand, the case that also derives a contradiction similarly.

Hence for every , i.e., .

[항상한상]

답변 달아주셔서 감사합니다.~~