| On the Global Dimension of Residue Rings |
| Received:December 16, 1989 |
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| 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 . |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.1991.04.020 |
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