论文标题
纯非IC领域的判别和积分基础
Discriminant and integral basis of pure nonic fields
论文作者
论文摘要
令$ k = \ q（θ）$是一个代数数字字段，$θ$满足不可约多的多项式$ x^{9} - a $ a $ a $ a $的$ \ q $ qu \ q $ $ \ z_k $表示$ k $ $ k $的代数整体环。在本文中，我们提供了每个素数的确切功能，该功率将$ \ z_k $中的子组$ \ z [θ] $的索引划分。此外，我们为每个Prime $ P $提供$ k $的$ P $构成基础。这些$ p $ - 综合基础导致建造$ k $的整体基础，并用示例说明。
Let $K = \Q(θ)$ be an algebraic number field with $θ$ satisfying an irreducible polynomial $x^{9} - a$ over the field $\Q$ of rationals and $\Z_K$ denote the ring of algebraic integers of $K$. In this article, we provide the exact power of each prime which divides the index of the subgroup $\Z[θ]$ in $\Z_K$. Further, we give a $p$-integral basis of $K$ for each prime $p$. These $p$-integral bases lead to a construction of an integral basis of $K$ which is illustrated with examples.
