| 多项式环的单位和稳定度的注记 |
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| 引用本文： | 崔书英,陈卫星. 多项式环的单位和稳定度的注记[J]. 大学数学, 2007, 23(1): 47-51 |
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| 作者姓名： | 崔书英 陈卫星 |
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| 作者单位： | 山东工商学院,数学与信息科学学院,烟台,264005;山东工商学院,数学与信息科学学院,烟台,264005 |
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| 基金项目： | This research was partially supported by the Doctorate Foundation of China Education Ministry （Grant No. 20020284009）. The authors wish to express their gratitude to Professor Wenting Tong and the referee for their helpful suggestions. |
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| 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.
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| 关 键 词： | 广义2-素环 多项式环 稳定度 |
| 文章编号： | 1672-1454（2007）01-0047-05 |
| 收稿时间： | 2005-07-04 |
| 修稿时间： | 2005-07-04 |
Notes on Units and Stable Ranges of Polynomial Rings |
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| CUI Shu-ying,CHEN Wei-xing. Notes on Units and Stable Ranges of Polynomial Rings[J]. College Mathematics, 2007, 23(1): 47-51 |
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| Authors: | CUI Shu-ying CHEN Wei-xing |
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| Abstract: | 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+…+anxn 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. |
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| Keywords: | generalized 2-primal rings polynomial rings stable ranges |
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