Accession Number : AD0264335

Title :   THE RING GENERATED BY THE Q-TH POWERS OF THE INTEGERS OF AN ALGEBRRAIC NUMBER FIELD, Q BEING A PRIME

Corporate Author : ILLINOIS UNIV URBANA

Personal Author(s) : BATEMAN,PAUL T. ; STEMMLER,ROSEMARIE S.

Report Date : DEC 1961

Pagination or Media Count : 1

Abstract : The following Theorem is proved: Let K be an algebraic number field of finite degree n over the rationals and let J (K) be its ring of integers. Let J sub q (K) be the additive group generated by the qth powers of the elements of J (K). Suppose q is a prime number, then J sub q (K) is equal to J (K), if and only if neither of the following circumstances obtains in K: (1) q is ramified in K, or (2) q is expressible in the form (p to the r power -1)/ (p to the d power -1), where p is a prime, r and d are positive integers, and p has in J (K) a prime ideal factor of degree r.

Descriptors :   *NUMBER THEORY, ALGEBRA

Distribution Statement : APPROVED FOR PUBLIC RELEASE