Matricial Representations of Reduplication Modulus Residue Rings
Fengchu Pan · College Mathematics · 2011
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}.