Understand why↗
When m is a prime number, mZ is a maximal ideal of Z because any ideal I containing mZ must be of the form kZ (since all ideals of Z are principal). The inclusion mZ ⊆ kZ implies that k divides m.
Conditions: The ambient ring is the ring of integers Z.; m is a prime number.; The ideal under consideration is mZ.
When m is a prime number, mZ is a maximal ideal of Z because any ideal I containing mZ must be of the form kZ (since all ideals of Z are principal). The inclusion mZ ⊆ kZ implies that k divides m.
Conditions: The ambient ring is the ring of integers Z.; m is a prime number.; The ideal under consideration is mZ.