| 重模剩余类环的矩阵表示 |
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| 引用本文： | 潘凤雏.重模剩余类环的矩阵表示[J].大学数学,2011,27(4):47-50. |
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| 作者姓名： | 潘凤雏 |
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| 作者单位： | [1]中国地质大学北京地球科学与资源学院,北京100083;[2]西藏地质调查院,拉萨850000 |
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| 摘 要： | 对模m的剩余类环Zm上的多项式环Zmx]中的任一n次（n≥1）首一多项式P,给出了重模剩余类环Zmx]/（P）到Zm上的n阶全矩阵环Mn（Zm）的一类单同态,从而实现了Zmx]/（P）的矩阵表示.若A为P的友矩阵,则Zmx]/（P）的矩阵表示为{an-1An-1＋…＋a1A＋a0E｜ai∈Zm,0≤i≤n-1}...
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| 关 键 词： | 重模剩余类环 矩阵表示 友矩阵 |
Matricial Representations of Reduplication Modulus Residue Rings |
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| PAN Feng-chu.Matricial Representations of Reduplication Modulus Residue Rings[J].College Mathematics,2011,27(4):47-50. |
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| Authors: | PAN Feng-chu |
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| Affiliation: | PAN Feng-chu1,2(1.School of Earth Sciences and Resources,China University of Geosciences,Beijing 100083,China,2.Institute of Geology Survey,Tibet,Lhasa 850000,China) |
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| Abstract: | Write Zm for the residue class ring of modulo m and P for any monic polynomial with degree n over polynomial ring Zmx].In this paper we presented a unitary homomorphism of reduplication modulus residue ring（quotient ring） Zmx]/（P）={b0＋b1x＋…＋bn-1xn-1｜bi∈Zm} onto the matrix ring Mn（Zm）,thus gave a matricial representation of reduplication modulus residue ring.If A is the companion matrix of polynomial P,then Zmx]/（P） can be expressed as the following form {an-1An-1＋an-2An-2＋…a1A＋a0E｜ai∈Zm,0≤i≤n-1}. |
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| Keywords: | reduplication modulus residue ring matricial representation companion matrix |
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