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Decomposition of Prime Ideal （p） in Q(μ1/17, ξ17) and Q(μ1/17)

Author: HeZuo
Tutor: GaoEnWei
School: Liaoning University
Course: Applied Mathematics
Keywords: prime ideal decomposition fully ramified prime complete splitting
CLC: O156.2
Type: Master's thesis
Year: 2011
Downloads: 27
Quote: 0
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Abstract


The decomposition of prime ideal is a very important research direction of the algebraic number theory. The question of decomposition of prime ideal （ p ） in the rational Galois extension number field is a very significant problem.In this paper ,we first make a detailed study of the question of decomposition of prime ideal （ p ） in the rational field extension Q （ξ1 7）and Q (μ1/17 ,ξ17).Second,we make a detailed study of the question of decomposition of prime ideal （ p ） in the rational field extension Q (μ1/17).We prove the decomposition of prime ideal （ p ） in Q (μ1/17) decided by the decomposition of p in Q (μ1/17).Let p to be the extension of p in the Q (μ1/17 ,ξ17).We discuss all of the decomposition styles of （ p ）in Q (μ1/17) and Q (μ1/17 ,ξ17) and solve the problem completely.In the first chapter,we give the summaries for the condition and the significance. We also give some research results both at home and abroad .In the second chapter,we give the basic definitions of the whole paper. In the third chapter,we give the theorems which is related to this paper .In the fourth chapter,we give the whole proofs and all of the possible decomposition styles.

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Number Theory > Algebraic number theory
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