Decomposition Of Prime Ideal （p） In Q(u^1/21)

The decomposition of prime ideal for the algebraic number theory is a very important research direction, studying of prime ideal decomposition problem is an important problem.At first,this paper discusses the prime ideal (p) in the Q(?21) for any expansion of the decomposition of Q(?3), then we discuss the prime ideal(p) in the7root dilatation Q(u1/7) problem of decomposition in the Q,we prove the prime number p for7root dilatation decomposition of the rational numbers field Q is composed of prime ideal (p) in any expansion A,which was determined by Q(u1/7,?3) decomposition of Q(?3)forms,we alse discuss the prime ideal(p) any expansion in Q(u1/7) in the Q(u1/21) decomposition problem. The last we discuss the prime ideal in any expansion of the decompositionin Q(u1/21) of extension of P in the Q(u1/7),all of the decomposition styles of (p) in Q(u1/21)was discussed and solve the problem completely.The first chapter, we introduce the prime ideal decomposition research in history and in the domestic and foreign research situation. The second chapter, we give the basi definition. The third chapter, we give the theorem which is related to the paper.At last, we give decomposition problem of the prime ideal (p) is shown in. Q(u1/21).