Number Fields by Daniel A. Marcus

Author:Daniel A. Marcus
Language: eng
Format: epub, pdf
Publisher: Springer International Publishing, Cham

(b)Suppose p is an odd prime not dividing m. Prove that p is unramified in L.

(c)Let Q be a prime of L lying over p (p as in (b)), and suppose . Use Theorem 33 to show that p splits into three primes in K.

(d)Determine how p splits in K for each of the possibilities for .

14.

Let , and fix a prime p in . Write , where . The Galois group of over is isomorphic to , which is isomorphic in a natural way to the direct product . Describe D and E (corresponding to p) in terms of this direct product.

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