关于n次代数数域的整数剩余类环上的CRT

对二次域R(m~(1/2))及n次域R(θ)上的整数模M的剩余类环I_M(0)上的DFT和CRT进行研究.主要工作有:1)将二次域上DFT的诸多已知结果全面地推广到模M为任意奇数的情形.2)在推广了的情形下,对I_M(θ)上的CRT和DFT的相互关系等问题作了逐一讨论,既包括定性的也包括定量的.3)利用在二次域上讨论中所采用的方法,把关于二次域的结果逐一推广到n次域上去.

ON THE CRT OVER A RESIDUE CLASSES RING OF ALGEBRAIC INTEGERS

Let IM(o) be a residue classes ring of integers in the n -th algebraic number field, where the modulo M is a natural mumber. In this note, we discuss the reversible transforms having cyclic convolution property (CRT's) and the Fourier-like transforms (DFT's) over the IM(0). Main results are thati) For the DFT over IM2(0), all results obtained for n =2 are extended to the general case in which the modulo M may be an arbitray odd number;ii) For the CRT over IM2(0), we give the necessary and sufficient conditions of existence as well as the numbers of all CRT's and all such CRT's which are not DFT;iii) All results of CRT and DFT over IM2(0) are extended to the case of IM2(0).