If is an ideal in a field , prove that or .
It can be proved or .
We shall use the following result to prove this.
Given is a ring with identity and is an ideal in .
If , then .
If , there is nothing to prove.
If , there exists such that .
Now, we know that is a field.
Therefore, must be a unit.
Hence, from the above result, we will conclude that .
Hence, or .
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