【摘要】 <正> 本文讨论了剩余类环R/I的整体同调维数.在§1中给出了R/I是平坦R—模的一个充要条件;然后在§2中主要证明了:若环R不含非零的单侧幂零理想,则(1)LGD(R/soc(_RR))≤LGD(R)≤LGD(R/soc(_RR))+1;(2)WD(R/soc(_RR))=WD(R).特别的对本原环和Von-Neumann正则环,上面的结果是成立的.更多还原

【Abstract】 If R/I is a flat R-module, the necessary-sufficient condition is given. Mo-reover, it is showh that the following two relations hold if a ring R has nonon-zero nilpotent one-sided ideals:( 1 ) LGD(R/Soc(R))≤LGD(R)≤LGD(R/Soc(R))+l ;(2) WD(R/Soc(R)) = WD (R).Particularly, the above relations holds for primitive rings and Von-Neumann regular rings .更多还原