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.
出处
《大学数学》
北大核心
2007年第1期47-51,共5页
College Mathematics
关键词
广义2-素环
多项式环
稳定度
generalized 2-primal rings
polynomial rings stable ranges
