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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. 相似文献
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证明了一般环I是Clean一般环当且仅当I上的形式幂级数一般环I[[x]]是Clean一般环;一般环I上的多项式环I[x]是Clean一般环当且仅当I是诣零的.引入了强Clean一般环的概念,它是强Clean环的推广.并证明了强π-正则的一般环是强Clean一般环. 相似文献
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In this note, a counterexample is given to show that a noncommutative VNL-ring need not be an SVNL-ring, answering an open question of Chen and Tong(Glasgow Math. J., 48(1)(2006)) negatively. Moreover, some new results about VNL-rings and GVNL-rings are also given. 相似文献
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Notes on Noncommutative VNL-rings and GVNL-rings 总被引:1,自引:0,他引:1
In this note, a counterexample is given to show that a noncommutative VNL-ring need not be an SVNL-ring, answering an open question of Chen and Tong (Glasgow Math. J., 48(1)(2006)) negatively. Moreover, some new results about VNL-rings and GVNL-ringsare also given. 相似文献
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