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Dihedral Quintic Fields with a Power Basis

Ashofteh, Somayeh | 2019

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 52612 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Jafari, Amir; Rajaei, Ali
  7. Abstract:
  8. An algebraic number field is a finite extension of Q. Let K be an algebraic number field. Each element 2 K satisfies an equation n + a1n1 + ::: + an with coefficients a1; :::; an 2 Q and is an algebraic integer if it satisfies such an equation with coefficients a1; :::; an 2 Z. algebraic integers form a subring.Let K be an algebraic number field of degree n. Let OK denote the ring of integers of K. The field K is said to possess a power basis if there exists an element 2 OK such that OK = Z + Z + + Zn1. A field having a power basis is called monogenic. In this thesis we consider that there exists infinitely many dihedral quintic fields with a power basis that is shown by lavallee [18]
  9. Keywords:
  10. Monogenic ; Numbers Field ; Integers Ring

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