Kummer函数域的理想类群

得到了二次函数域的理想类群的２－秩公式和一般ｌ次Ｋｕｍｍｅｒ函数域理想类群ｌ－秩的下界。由此完全确定出类数不被ｌ整除的所有ｌ次Ｋｕｍｍｅｒ函数域。其次，还证明了不存在这样的ｌ次Ｋｕｍｍｅｒ函数域，其理想类群的ｌ－Ｓｙｌｏｗ子群为ｌ＾ｎ阶循环群。

The Ideal Class Groups of Kummer Function Fields

The author obtained an explicit 2-rank formula for the ideal class groups of quadratic function fields and also get a lower bound for the l-rank of the ideal class groups of l-th Kummer function fields.Consequently,the author determined all l-th Kummer function fields whose ideal class numbers are prime to l.It′s also proved that if the l-Sylow subgroup of the ideal class group of a l-th Kummer function field is cyclic then it must be of order l.