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| ON EULER CHARACTERISTIC OF MODULES |
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Citation： |
Tong Wenting.ON EULER CHARACTERISTIC OF MODULES[J].Chinese Annals of Mathematics B,1989,10(1):58~64 |
| Page view： 820
Net amount： 810 |
Authors： |
Tong Wenting; |
Foundation： |
The Project supported by National Natural Science Foundation of China. |
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| Abstract： |
This paper gives a characteristic property of the Euler characteristic for IBN rings. The following results: are proved. (1) If R is a commutative ring, M, N are two stable free R-modules, then $\[\chi (M \otimes N) = \chi (M)\chi (N)\]$, where $\[\chi \]$ denotes the Euler characteristic. (2)
If $\[f:{K_0}(R) \to Z\]$ is a ring isomorphism, where $\[{K_0}(R)\]$ denotes the Grothendieck group of R, $\[{K_0}(R)\]$ is a ring when R is comnmtative, then $\[f([M]) = \chi (M)\]$ and $\[\chi (M \otimes N) = \chi (M)\chi (N)\]$
when M,N are finitely generated projective R-modules, where the isomorphism class [M] is a generator of $\[{K_0}(R)\]$. In addition, some applications of the results above are also obtained. |
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