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Mat. Zametki, 1973, Volume 14, Issue 3, Pages 399–406 (Mi mz7270)  

On the global dimension of an algebra

V. E. Govorov

Moscow Institute of Electronic Engineering

Abstract: Let algebra $R=\Lambda/P$, where $\operatorname{w. gl. dim}R:=\{\min n|_{\forall R}-modules X,Y$, $\operatorname{Tor}_{n+1}^R(X,Y)=0\}$. 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:
$$ AP^n\cap P^nB=AP^nB+P^{n+1} \quad (AP^nB\cap P^{n+1}=AP^{n+1}+P^{n+1}B). $$


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English version:
Mathematical Notes, 1973, 14:3, 789–792

Bibliographic databases:

UDC: 519.4
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

Citation in format AMSBIB
\Bibitem{Gov73}
\by V.~E.~Govorov
\paper On the global dimension of an algebra
\jour Mat. Zametki
\yr 1973
\vol 14
\issue 3
\pages 399--406
\mathnet{http://mi.mathnet.ru/mz7270}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=330225}
\zmath{https://zbmath.org/?q=an:0281.16017}
\transl
\jour Math. Notes
\yr 1973
\vol 14
\issue 3
\pages 789--792
\crossref{https://doi.org/10.1007/BF01147457}


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