Understand why↗
The zero ideal is a maximal ideal of a field because a field has no nontrivial ideals. The only ideals of a field F are the zero ideal {0} and the unit ideal F itself.
Conditions: The ambient ring F is a field.; The ideal under consideration is the zero ideal {0}.
The zero ideal is a maximal ideal of a field because a field has no nontrivial ideals. The only ideals of a field F are the zero ideal {0} and the unit ideal F itself.
Conditions: The ambient ring F is a field.; The ideal under consideration is the zero ideal {0}.