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This article is cited in 1 scientific paper (total in 1 paper)
On the global dimension of an algebra
V. E. Govorov Moscow Institute of Electronic Engineering
Abstract:
Let algebra $R=\Lambda/P$, where $\operatorname{w. gl. dim}R:=\{\min n|_{\forall R}\text{-modules }X,Y$, $\operatorname{Tor}_{n+1}^R(X,Y)=0\}$. In order that $\operatorname{w. gl. dim}R\le2n$ ($\operatorname{w. gl. dim}R\le2n+1$), it is necessary and sufficient that, for any two ideals of algebra $\Lambda$, a left ideal $A$ and a right ideal $B$, containing ideal $P$, the following equation holds:
$$
AP^n\cap P^nB=AP^nB+P^{n+1} \quad (AP^nB\cap P^{n+1}=AP^{n+1}+P^{n+1}B).
$$
Received: 10.04.1972
Citation:
V. E. Govorov, “On the global dimension of an algebra”, Mat. Zametki, 14:3 (1973), 399–406; Math. Notes, 14:3 (1973), 789–792
Linking options:
https://www.mathnet.ru/eng/mzm7270 https://www.mathnet.ru/eng/mzm/v14/i3/p399
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