Could anyone give me a reference for the proof of “ In a commutative artinian ring, every maximal ideal is a minimal prime ideal and every minimal prime ideal is a maximal ideal” ?

  • $\begingroup$ Atiyah's introduction to commutative algebra:commutative ring is Artinian ring iff it is Noetherian ring and the Krull dimension is zero. $\endgroup$ – Sky Jan 26 '18 at 11:07
  • $\begingroup$ How this is relevant ? $\endgroup$ – Math90 Jan 26 '18 at 11:20
  • $\begingroup$ you can find the definition of Krull dimension in Wikipedia. $\endgroup$ – Sky Jan 26 '18 at 11:24
  • $\begingroup$ What is your definition of Artinian ring? $\endgroup$ – lhf Jan 26 '18 at 11:36
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    $\begingroup$ See math.stackexchange.com/questions/27145/… $\endgroup$ – lhf Jan 26 '18 at 12:47

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