Maximal_Ideal_iff_Quotient_Ring_is_Field

Let $\struct {R, +, \circ}$ be a commutative ring with unity whose zero is $0_R$ and whose unity is $1_R$. Let $J$ be an ideal of $R$. The following are equivalent $(1): \quad$ $J$ is a maximal ideal. $(2): \quad$ The quotient ring $R / J$ is a field.