多项式环的单位和稳定度的注记(英文)  

Notes on Units and Stable Ranges of Polynomial Rings

作　　者：崔书英[1] 陈卫星[1] 

机构地区：[1]山东工商学院数学与信息科学学院,烟台264005

出　　处：《大学数学》2007年第1期47-51,共5页College Mathematics

摘　　要：称环R为广义2-素环,如果R的幂零元集与上诣零根一致.证明了R上的多项式为单位当且仅当它的常数项是R中的单位而其它系数是幂零的.因此,广义2-素环上的多项式环的稳定度大于一.Rings considered are associative with identity. In this note, a ring R is defined to be generalized 2-primal if the set of nilpotent elements in R coincides with its upper nil radical. It is proved that＇a polynomial f（x）=a0＋a1x＋…＋anx^n over a generalized 2-primal ring R is a unit in R[x] if and only if a0 is a unit in R and ai is nilpotent for each i≥1. Hence the stable range of R[x] is always greater than one for any generalized 2-primal ring R.

关 键 词：广义2-素环 多项式环 稳定度 

分 类 号：O153.3[理学—数学]