A fractional ideal is a generalization of an ideal in a ring R. Instead, a fractional ideal is contained in the number field F, but has the property that there is an element b element R such that a = b f = {b x such that x element f} is an ideal in R. In particular, every element in f can be written as a fraction, with a fixed denominator. f = {a/b such that a element a} Note that the multiplication of two fractional ideals is another fractional ideal.

class group | ideal | number field