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On the arithmetic of the endomorphism ring End($mathbb{Z}_{p} imesmathbb{Z}_{p^{m}}$) | | Xiusheng Liu
; Hualu Liu
; | | Date: |
3 May 2016 | | Abstract: | For a prime $p$, let
$E_{p,p^m}={egin{pmatrix}a&b\p^{m-1}c&dend{pmatrix}|a,b,cinmathbb{Z}_{p},~mathrm{and}~din
mathbb{Z}_{p^{m}}}$. We first establish a ring isomorphism from
$mathrm{End}(mathbb{Z}_p imesmathbb{Z}_p^m)$ onto $E_{p,p^m}$. We then
provide the way to compute $-d$ and $d^{-1}$ using arithmetic in
$mathbb{Z}_{p}$ and $mathbb{Z}_{p^{m}}$, and characterize invertible elements
in $E_{p,p^m}$. Moreover, we introduce the minimal polynomial for each element
in $E_{p,p^m}$ and given its applications. | | Source: | arXiv, 1605.0805 | | Services: | Forum | Review | PDF | Favorites | |
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