 Ideal number: Encyclopedia II - Ideal number - ExampleFor instance, let y be a root of y2 + y + 6 = 0, then the ring of integers of the field is , which means all a + by with a and b integers form the ring of integers. An example of a nonprincipal ideal in this ring is 2a + yb with a and b integers; the cube of this ideal is principal, and in fact the class group is cyclic of order three. The corresponding class field is obtained by adjoining an element w satisfying w3 - w - ...
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