
Accession Number : AD0264335
Title : THE RING GENERATED BY THE QTH 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