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Essential Dimension

Moghimypour, Mohammad Benyamin | 2016

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 48020 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Mahdavi Hezavehi, Mohammad
  7. Abstract:
  8. Our main purpose is introducing essential dimension and investigating properties of this concept and definition of it on different algebraic objects and proving some theories about it. In the beginning we define the concept of essential dimension on the extension fields which indeed it is expressing complexity of extension on the background field.Then with the meaning of noetherian extension which we will introduce it in the chapter three, we generalize the concept of essential dimension to finite groups. At last we investigate the connection between the essential dimension with generic polynomials and one of our important results is finding upper bounds for essential dimension of finite groups
  9. Keywords:
  10. Algebra ; Field Extension ; Finite Group ; Essential Dimention ; Noetherian Extension

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