Decomposition Of Prime Ideal (P) In Q(u^1/2m)

Since Kummer gave the definition of ideal and Dedekind developed the theory of ideal,Prime ideal decomposition is an important problem in algebraic number the- ory which has extensive application of the Diophantine Equation and the class field theory.Especially,it is helpful to solve some unsolved problems in the Diophantine Equation.Hence it is significant to factorize the prime ideal of Q in its finite extension field.Assume that Q is the field of rational numbers and ( p ) is Q prime ideal.There are two ways to factorize the prime ideal of Q in its finite extension field.One is extension and moving,the other is local-integral ideal.In this paper,we will discuss the problem of the law of decomposition of prime ideal ( p ) in Q(u^2m/1) using the method of local field(where m is an odd prime).Moreover the possible type of decomposition of prime ideal has been established.