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The zero ideal {0} is not a maximal ideal of Z because every ideal of Z contains the integer 0, and therefore contains {0}. This means {0} can be properly contained in a larger ideal, violating the definition of a maximal ideal.

Conditions: The ambient ring is the ring of integers Z.; The ideal under consideration is the zero ideal {0}.

The zero ideal {0} is not a maximal ideal of Z because every ideal of Z contains the integer 0, and therefore contains {0}. This means {0} can be properly contained in a larger ideal, violating the definition of a maximal ideal.

Conditions: The ambient ring is the ring of integers Z.; The ideal under consideration is the zero ideal {0}.