proof-that-if-R-is-a-commetative-ring-with-unity-then-an-ideal-M-and-R-is-maximal-iff-R-M-is-a-field-

Question Number 134831 by abdurehime last updated on 07/Mar/21

$${proof}\:{that}\:{if}\:\mathrm{R}\:\mathrm{is}\:\mathrm{a}\:\mathrm{commetative}\:\mathrm{ring}\:\mathrm{with}\:\mathrm{unity}\:\mathrm{then}\:\mathrm{an}\:\mathrm{ideal}\: \\ $$$$\mathrm{M}\:\mathrm{and}\:\mathrm{R}\:\mathrm{is}\:\mathrm{maximal}\:\mathrm{iff}\:\frac{\mathrm{R}}{\mathrm{M}}\:\mathrm{is}\:\mathrm{a}\:\mathrm{field}. \\ $$

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