摘要
对模m的剩余类环Zm上的多项式环Zm[x]中的任一n次(n≥1)首一多项式P,给出了重模剩余类环Zm[x]/(P)到Zm上的n阶全矩阵环Mn(Zm)的一类单同态,从而实现了Zm[x]/(P)的矩阵表示.若A为P的友矩阵,则Zm[x]/(P)的矩阵表示为{an-1An-1+…+a1A+a0E|ai∈Zm,0≤i≤n-1}.
Write Zm for the residue class ring of modulo m and P for any monic polynomial with degree n over polynomial ring Zm[x].In this paper we presented a unitary homomorphism of reduplication modulus residue ring（quotient ring） Zm[x]/（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 Zm[x]/（P） can be expressed as the following form {an-1An-1＋an-2An-2＋…a1A＋a0E｜ai∈Zm,0≤i≤n-1}.
出处
《大学数学》
2011年第4期47-50,共4页
College Mathematics
关键词
重模剩余类环
矩阵表示
友矩阵
reduplication modulus residue ring
matricial representation
companion matrix
