Understand why↗
The zero ideal {0} is a prime ideal of Z because it satisfies the definition of a prime ideal. First, {0} is a proper ideal of Z (since {0} ≠ Z).
Conditions: The ambient ring is the ring of integers Z.; The ideal under consideration is the zero ideal {0}.
The zero ideal {0} is a prime ideal of Z because it satisfies the definition of a prime ideal. First, {0} is a proper ideal of Z (since {0} ≠ Z).
Conditions: The ambient ring is the ring of integers Z.; The ideal under consideration is the zero ideal {0}.