论文标题
$ \ Mathbb z [t]/（t^4）$的子环
Subrings of $\mathbb Z[t]/(t^4)$
论文作者
论文摘要
在本说明中，我们研究了$ \ mathbb z [t]/（t^4）$的子环的分布，并证明了两个结果。第一个结果给出了一个有界索引的$ \ mathbb z [t]/（t^4）$的子环数的渐近公式。该定理的证明方法是$ p $ - adic集成a la grunewald，segal和Smith。我们的第二个结果是关于在$ \ mathbb z [t]/（t^4）$中的Cocyclic子环的分布。我们对此结果的证明是组合，基于对某些类别的特殊形式的史密斯正常形式计数某些类别的矩阵。
In this note we study the distribution of the subrings of $\mathbb Z[t]/(t^4)$ and prove two results. The first result gives an asymptotic formula for the number of subrings of $\mathbb Z[t]/(t^4)$ of bounded index. The method of proof of this theorem is $p$-adic integration a la Grunewald, Segal, and Smith. Our second result is about the distribution of cocyclic subrings in $\mathbb Z[t]/(t^4)$. Our proof of this result is combinatorial and is based on counting certain classes of matrices with Smith normal forms of a special form.
