On the arithmetic of the endomorphism ring End(${\mathbb{Z}}_p\times {\mathbb{Z}}_{p^m}$)

Xiusheng Liu, Hualu Liu

For a prime $p$, let $E_{p,p^m}=\{\left(\begin{array}{cc}a& b\\ p^{m-1}c& d\end{array}\right)|a,b,c\in {\mathbb{Z}}_p,\mathrm{and}d\in {\mathbb{Z}}_{p^m}\}$. We first establish a ring isomorphism…