论文标题
实际二次场的立方和四分之一扩展的功率积分基础
Power integral bases in cubic and quartic extensions of real quadratic fields
论文作者
论文摘要
对单基因和功率积分基库的研究最近从绝对情况（Q）扩展到相对情况（代数数字段）。以前，在相对情况下，我们只能在地下场是一个假想的二次场时才能成功计算功率积分碱基的发生器。这是在更困难的情况下，在实际二次场的扩展中考虑单基因的第一种情况。我们提供了有效的算法，用于计算实际二次场的立方和四分之一扩展中的功率积分碱基的发生器，更准确地使用具有真实二次场的立方和四分之一场的复合材料。如果四分之一的字段完全复杂，我们提出了一种特别简单的算法。我们用两个详细的示例说明了我们的方法。
Investigations of monogenity and power integral bases were recently extended from the absolute case (over Q) to the relative case (over algebraic number fields). Formerly, in the relative case we only succeeded to calculate generators of power integral bases when the ground field is an imaginary quadratic field. This is the first case when we consider monogenity in the more difficult case, in extensions of real quadratic fields. We give efficient algorithms for calculating generators of power integral bases in cubic and quartic extensions of real quadratic fields, more exactly in composites of cubic and quartic fields with real quadratic fields. In case the quartic field is totally complex, we present an especially simple algorithm. We illustrate our method with two detailed examples.
