The Decomposition Of Prime Idea P In Composite Field Q(d^1/2,m^1/3)

The problems of the decomposition of prime ideal and the integral basis of an algebraic number field is very important in the algebraic number theory. The integral basis of quadratic field and pure cubic field have been solved completely,and the decomposition of prime ideal in quadratic field and pure cubic field also have been solved,but the decomposition of prime ideal and the integral basis of a general algebraic number field is not clear.Let Q((?)) be a quadratic field,we suppose that d is squarefree, d∈Z*.Q((?))is a cubic field we suppose that m is cube-free, m∈Z. Algebraic number field Q((?)) is a composite field.There are two parts in this paper. In the first part we mainly study the decomposition of prime ideal in a composite field, for the decomposition of prime ideal in quadratic field and pure cubic field also have been solved,on the base of theory of decomposition of prime ideal in quadratic field and pure cubic field,we discuss the decomposition of prime idea in composite field Q((?),(?))and have got some achievements. In the second part of this paper, we discusses problems of integral basis and discriminant of the composite field Q((?),(?)).