分圆域[Cyclotomic Field] - 达人(其实～我是卧底，来自外星)

2005/08/27 | 分圆域[Cyclotomic Field]
类别(∑〖数学〗) | 评论(0) | 阅读(63) | 发表于 09:34: A cyclotomic field is obtained by adjoining a primitive root of unity , say , to the rational numbers . Since is primitive, is also an th root of unity and contains all of the th roots of unity

For example, when and , the cyclotomic field is a quadratic field

The Galois group of a cyclotomic field over the rationals is the multiplicative group of , the ring of integers (mod ). Hence, a cyclotomic field is a Abelian extension. Not all cyclotomic fields have unique factorization, for instance, where .; 0