Saputra, Sofyan (2015) FAKTORISASI PADA LAPANGAN QUADRATIC Q[√d]. Fakultas Matematika dan Imu Pengetahuan Alam, Universitas Lampung.
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Abstract
ABSTRAK Untuk bilangan bulat kuadrat bebas d selain 1, Misalkan, K=Q[√d]={x+y√d:x,y∈Q} Selanjutnya K disebut lapangan . kuadratik atau bilangan rasional Q. Kita akan mendefinisikan konsep bilangan bulat untuk K, seperti konsep bilangan bulat biasa Z pada bilangan rasional Q. Bentuk bilangan dari K adalah {a+b√d:a,b∈Z} jika d≢1 mod 4 dan {a+b((1+√d)/2):a,b∈Z} jika d≡1 mod 4 Untuk α∈K , himpunan Tr(α)=αα ̅ dan N(α)=αα ̅ masing-masing disebut trace dan norm dari.α . Selanjutnya O_k dinotasikan sebagai himpunan dari bilangan bulat di K. Faktorisasi tunggal dari bilangan bulat pada K tidak terlalu terpenuhi. Konsep norm memegang peranan penting dalam hal ini. Jika α∈O_k mempunyai norm yang prima dalam Z, maka α irreducible dalam O_k. Key Words : kuadrat bebas , lapangan kuadratik , bilangan bulat di K , trace , norm , prima , irreducible ABSTRACT FACTORIZATION IN QUADRATIC FIELD Q[√d] By SOFYAN SAPUTRA For a square free integer d other than 1, Let, K=Q[√d]={x+y√d:x,y∈Q} This is called a quadratic field and it has degree 2 over Q. We will define a concept of “integer” for K, which will play the same role in K as the ordinary integers Z do in Q. The integer of K are {a+b√d:a,b∈Z} if d≢1 mod 4 and {a+b((1+√d)/2):a,b∈Z} if d≡1 mod 4 For α∈K , set Tr(α)=αα ̅ and N(α)=αα ̅ . These are called the trace and norm of α . We denote the integers of K as O_k. Unigue factoritation in the integers of K does not always hold. The norm will play important role. If α∈O_k has norm which is prime in Z, then α is irreducible in O_k. Key Words : square integer , quadratic field , integer of K , trace , norm , prime, irreducible.
| Item Type: | Other |
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| Subjects: | Q Science (General) > QA Mathematics |
| Divisions: | Fakultas MIPA > Prodi Matematika |
| Depositing User: | 8967880 . Digilib |
| Date Deposited: | 20 Feb 2015 04:11 |
| Last Modified: | 20 Feb 2015 04:11 |
| URI: | http://digilib.unila.ac.id/id/eprint/7182 |
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