2KEITHCONRAD2.ProofsNowweproveTheorem1.1.Proof.LetpbeaprimeidealofOKth - PDF document

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2KEITHCONRAD2.ProofsNowweproveTheorem1.1.Proof.LetpbeaprimeidealofOKth - PPT Presentation

4KEITHCONRADProofLetfT2OKTbeEisensteinatsomeprimeidealIffTisreducibleinKTthenfTgThTforsomenonconstantgTandhTinKTWerstshowthatgandhcanbechoseninOKTAsfismonicwecanassumegand ID: 148133

4KEITHCONRADProof.Letf(T)2OK[T]beEisensteinatsomeprimeideal.Iff(T)isreducibleinK[T]thenf(T)=g(T)h(T)forsomenonconstantg(T)andh(T)inK[T].WerstshowthatgandhcanbechoseninOK[T].Asfismonic wecanassumegand

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