: 𝑹𝑴⁄is a field if and only if 𝑴 is a maximal ideal of 𝑹.
Theorem: Let 𝑹 be a commutative ring with unity, and let 𝑴 be an ideal of 𝑅. Then 𝑹𝑴⁄is a field if and only if 𝑴 is a maximal ideal of 𝑹.
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