Abstract
For a prime p, let \({E_{P,{P^m}}} = \left\{ {\left( {\begin{array}{*{20}{c}} aamp;b \\ {{p^{m – 1}}c}amp;d \end{array}} \right)\left| {a,b,c \in {Z_p},d} \right. \in {Z_{{p^m}}}} \right\}\). We first establish a ring isomorphism from \({Z_{p,{p^m}}}\) onto \({E_{p,{p^m}}}\). Then we provide a way to compute -d and d–1 by using arithmetic in Zp and \({Z_{{p^m}}}\), and characterize the invertible elements of \({E_{p,{p^m}}}\). Moreover, we introduce the minimal polynomial for each element in \({E_{p,{p^m}}}\)and give its applications.
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Foundation item: Supported by the Research Project of Hubei Polytechnic University (17xjz03A)
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Liu, X., Liu, H. & Hu, P. On the Arithmetic of Endomorphism Ring End\(({Z_p} \times {Z_{{p^m}}})\). Wuhan Univ. J. Nat. Sci. 23, 277–282 (2018). https://doi.org/10.1007/s11859-018-1322-1
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DOI: https://doi.org/10.1007/s11859-018-1322-1