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Prove or disprove that the existence of an integral domain of order 4 that is not a field.

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Prove or disprove that the existence of an integral domain of order 4 that is not a field.

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Solution Summary

It is disproven that the existence of an integral domain of order 4 that is not a field. Inverse nonzero elements of R is analyzed.

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Answer: It does not exist an integral domain of order 4 that is not a field.

Suppose R is an integral domain with order 4, then I claim that R must be a field.
We know, an integral domain is a ...

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