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Integral domain

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There is integral domain with exactly six elements. Disprove or Prove

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Solution Summary

This is a proof regarding integral domain with six elements.

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Suppose R is an integral domain with |R|=6. By the definition, R contains two element 1 and 0 where 1 is the multiplication identity and 0 is the addition identity and 1 is not equal to 0. R does not have zero factors.
We consider its zero idea Z=(0).
If Z=(0) is a maximal ideal of R, ...

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