Theorem on Maximal Ideal An ideal M is maximal ideal of R iff R/M is field

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M is a maximal ideal of a ring R if and only if R/M is a field. Lecture 12. M is a maximal ideal of a ring R if and only if R/M is a field. Lecture 12.
I is a Maximal Ideal iff R/I is a Field Proof I is a Maximal Ideal iff R/I is a Field Proof
Proof: Prime Ideal iff R/P is Integral Domain; Maximal iff R/M is Field Proof: Prime Ideal iff R/P is Integral Domain; Maximal iff R/M is Field
R/M is Field iff M is maximal ideal(Imp Theorem) R/M is Field iff M is maximal ideal(Imp Theorem)
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