Devison Rings of Degree Pn<br/>

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Devison Rings of Degree Pn

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 41428 (02)
University: Sharif University of Technology
Department: Mathematical Science
Advisor(s): Mahdavi Hezavehi, Mohammad
Abstract:
Albert proposed the cyclic algebraof the degree 4 in1934. After that more studies were conducted on thecyclic algebras on F in conditions in which L = F(µ )nis an extention of F, for in the Albert’s example it wasmanifest that 2|[F(µ ) : F]. In a paper in the same yearnAlbert proposed a condition for an F-division algebrato be cyclic. In this thesis, a theorem will be proposedin which for the condition (n=1) the Albert’s theoremwill be the result. Moreover, F-division rings of the pndegree are investigated. the required means is modularspectral factorization which was for the ?rst time de?nedin clusters by Merkuryev. Finally a condition will beproposed for the fact that F-division algebra of pn degrrebe cyclic
Keywords:
Division Rings ; Cyclic Algebra ; Non Cyclic Algebras ; Algebra Modular Spectral ; Division Algebras of Degree Pn

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