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On a Number-Theoretic Result of Sylvester-Kronecker-Zsigmondy

โœ Scribed by G. Steidl; M. Tasche

Publisher
John Wiley and Sons
Year
1989
Tongue
English
Weight
713 KB
Volume
140
Category
Article
ISSN
0025-584X

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โœฆ Synopsis

Let K be an algebraic extension field of Q . Further. let CIc be the domain of algebraic integers of K , and let @,(x) be the n-th cyclotomic ~iolynomial. This paper is devoted to the factorization of the principal ideal sPn(c) DK ( e E QI{) into prime ideals of s),c. The main result (Theorem 3.4) cnn be considered as A generalization of a known result of SYLVESTER, KRONECEER and ZSIGMONDY on the prime factorization of @,(e) ( e E Z). With Theorem 3.4., we improve corresponding results of REDEI [ll] and SACHS [14]. We generalize a technique developed in [ 8 ] and [3] and we study also the cases that 1. is a quadratic field and a cyclotomic field, respectively. Finally, we apply the results to the parameter determination of FonmR-Like number-theoretic transforms in k ? ~.

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