I is a Maximal Ideal iff R/I is a Field Proof

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I is a Maximal Ideal iff R/I is a Field Proof
  1. The Math Sorcerer
  2. Maximal Ideal
  3. Ideal
  4. Field
  5. Abstract Algebra (Field Of Study)
  6. Mathematics (Field Of Study)
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Комментарии
Автор

Thanks so much. It is by far the best proof for this theorem that I have seen. No fancy homeomorphisms, no weird generators or other theorems, simply beautiful. Thanks.

Tolsimir
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Thanks so much for helping me with algebra homework!

lipstickaddicted
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Please, I need your help in solving this proof. Can I communicate with you? I am from Iraq

if M is maximal ideal of S and f is homo and onto then f inverse of M is maximal ideal of R 🙏

Fatima-nntv
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Hi, Right at the beginning we assumed that x does not belong to J. Thats why (J+x)(J+y)=(J+1) made sense. If x belongs to J, then (J+x) equals 0. Now at the end when you are writing 1 in a creative way i.e. 1 = xy - (xy-1) you are asserting that x belongs to J. Am I missing something here. Understood the first half of the proof completely and second half also until the end where its not making sense. Somebody please help.

ShwetankT
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Can you solve this question by charpits method
P²-q²= x-y/z

Anjali._So