首系数为环上单位的多项式的刻画  

Portray of polinomial whose leading coefficient is unit in ring

作　　者：刘英[1] 王路群[1] 李凤霞[1] 

机构地区：[1]哈尔滨师范大学恒星学院,哈尔滨150025

出　　处：《黑龙江大学自然科学学报》2010年第2期193-196,共4页Journal of Natural Science of Heilongjiang University

基　　金：黑龙江省高教学会"十一五"规划项目(115C-580)

摘　　要：对于含1环R上的一元多项式环R[x],给出R[x]中施行带余除法的一个充要条件并建立商、余式的显式表达式,进而利用矩阵去刻画多项式整除,并给出交换环上方阵的Hamilton-Cayley定理,完全推广了域上多项式环的相应结论。For a polynomial ring R[x] of a ring R with 1, sufficient and necessary conditions are given to guaranteeing that division algorithm can be proceeded between polynomials in R [ x ], and explicit expressions of quotient and remainder are established. Furthermore, polynomials divisibility is expressed by matrices and Hamilton-Cayley theorem over a commutative ring is given, which generalize the corresponding results of the polynomial ring over a number field.

关 键 词：含1环 单位 多项式 带余除法 

分 类 号：O151.21[理学—数学]