Decomposition Of Prime Ideal P In F=Q(ξ₇+ξ₇^-1)over F(μ^1/7)

Algebraic number theory is the study of algebraic number field and a knowledge of algebraic integer. It is a very important topic that decomposition of prime ideal in algebraic number theory. Especially important to judge lots of the issue of decomposition of prime ideal in the limited extended.In this paper, through studying other decomposition based on the theory of prime ideal, the decomposition of prime idealP in F=Q(ξ+7) over F(7√μ) has been resolved and discussed.The first part, we give the summarize for the signficance and the achievement. The second part, we offer the preparation knowledge of all the paper and reveal in detail the source of the decomposition of prime ideal. The third part, we adopting the method of expansion of translation to resolve the prime ideal P in F=Q(ξ+ξ7-1) over F(7√μ) has been discussed. The fourth part, it is the summary of conclusion in the article.