| Algebraic number theory is a science which researches algebraic number field (that is finite extension of rational field) and algebraic number integer. The prime ideal decomposition of algebraic number theory as an important research issue has been the focus of attention.On the basis of my tutor's research, this paper gives the decomposition of prime ideal (p) in Q(μ23), and proves the decomposition of prime ideal (p) in Q(μ23) is determined by the decomposition of any extension in Q(μ23,ξ23) of prime ideal (p) in Q(ξ23).There are four parts in this paper.The first chapter is introduction part, we give the summary for the condition and the significance of the decomposition of prime ideal.And summarize the realistic and theory the decomposition of prime ideal. The second chapter, we give the preparation knowledge, including the definition and concept of the decomposition of prime ideal. The third chapter, we give a whole proof by the knowledge and proposition that the second part was given. The fourth chapter is the conclusion and prospect. |
