Decomposition Of Prime Ideal (p) In Q(μ^1/17, ξ₁₇) And Q(μ^1/17)

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 (μ^1/17 ,ξ₁₇).Second,we make a detailed study of the question of decomposition of prime ideal ( p ) in the rational field extension Q (μ^1/17).We prove the decomposition of prime ideal ( p ) in Q (μ^1/17) decided by the decomposition of p in Q (μ^1/17).Let p to be the extension of p in the Q (μ^1/17 ,ξ₁₇).We discuss all of the decomposition styles of ( p )in Q (μ^1/17) and Q (μ^1/17 ,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.