# Integral domain

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

Â© BrainMass Inc. brainmass.com March 6, 2023, 1:24 pm ad1c9bdddfhttps://brainmass.com/math/integrals/integral-domain-21829

#### Solution Preview

Disprove

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, ...

#### Solution Summary

This is a proof regarding integral domain with six elements.

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