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| NOETHERIAN GR-REGULAR RINGS ARE REGULAR |
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Citation： |
Li Huishi.NOETHERIAN GR-REGULAR RINGS ARE REGULAR[J].Chinese Annals of Mathematics B,1994,15(4):463~468 |
| Page view： 1055
Net amount： 768 |
Authors： |
Li Huishi; |
Foundation： |
Project supported by the Science
Foundation of State Education Committee |
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| Abstract： |
It is proved that for a left Noetherian $\Bbb Z$-graded ring $A$, if every
finitely generated graded $A$-module has finite projective dimension
(i.e., $A$ is gr-regular) then every finitely generated
$A$-module has finite projective dimension (i.e., $A$ is regular).
Some applications of this result to filtered rings and some classical cases
are also given. |
Keywords： |
Graded ring, Regular ring, Projective dimension. |
Classification： |
16W50, 26E10. |
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