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Math Help - Ideals of Integral Domains

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    Ideals of Integral Domains

    Let D be an integral domain which is not a field. Show that {0} is a prime, but not a maximal, ideal of D.
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    Quote Originally Posted by Coda202 View Post

    Let D be an integral domain which is not a field. Show that {0} is a prime, but not a maximal, ideal of D.
    {0} being prime is just the definition of an integral domain. if {0} was a maximal ideal, then D would be a domain with no non-zero proper ideal and hence it'd be a field.
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