Question

Prove that an ideal M in a commutative ring with unit element is maximal if and only if R/M is a field.

Answer 1

Answer:

Theorem 3.4. 2 Let R be a commutative ring with identity, and let M be an ideal of R. Then the factor ring R/M is a field if and only if M is a maximal ideal of R. (a + M)(b + M) = 1 + M in R/M.