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Ring Kuosen dari Ring Polinomial

Ring Kuosen dari Ring Polinomial. Polinomial irredusibel dalam suatu ring polinomial dapat dianalogikan dengan bilangan prima. Di samping itu dalam himpunan bilangan Z setiap ideal merupakan ideal utama ( m ).

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Ring Kuosen dari Ring Polinomial

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  1. Ring Kuosendari Ring Polinomial

  2. Polinomialirredusibeldalamsuatu ring polinomialdapatdianalogikandenganbilangan prima. • Di sampingitudalamhimpunanbilanganZsetiap ideal merupakan ideal utama (m). • Dalambabiniakandibahasuntukkelas ring manakahdarikoefisien-koefisiendaripolinomial yang beradadalamAsehinggasetiap ideal dalamA[x] merupakan ideal utama? • Sifat yang tertulisdalamteoremainisangatpentingdalampembahasanselanjutnya.

  3. Teorema XVI.1 • JikadiketahuiF field makasetiap ideal dalamF[x] merupakan ideal utama. Contoh XVI.1 • Diketahui ring R[x] dan ideal • (x2 + 1) = { f(x) (x2 + 1)│f(x) dalamR[x] } • Akanditentukansifat-sifatdariR[x] / (x2 + 1).

  4. Teorema XVI.2 • JikaF field danpolinomialp(x) irredusibeldalamF[x] maka ring kuosenF[x] / ( p(x) ) merupakan field. Teorema XVI.3 (Teorema fundamental darihomomorfisma ring) • Jikadiketahuif : A → Bhomomorfisma ring denganpetaf(A) danintiKmaka ring kuosenA/Kisomorfismadenganf(A).

  5. Latihan

  6. TERIMA KASIH

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