一些循环代数函数域的不分明理想类（英文）

AMBIGUOUS CLASSES OF SOME CYCLIC ALGEBRAIC FUNCTION FIELDS

本文研究了一些l次循环函数域的理想类群的不分明理想类的结构问题.利用函数域的素理想分解理论和理想的一阶上同调理论,得到了这几类循环函数域的理想类群的l-秩的下界.进一步,我们还得了一些不分明理想类中不含不分明理想的域的充分条件.

We study the structure of some kinds of cyclic function fields with degree l. By the means of prime ideal decomposition and the computation of first cohomology of the ideal class group,we get the lower bound of the l-ranks of the class group of these function fields. In addition,we find a necessary condition on when these kinds of fields have ambiguous class containing no ambiguous ideals.