J. Aust. Math. Soc.  74 (2003), 235-238
On $\mathfrak{F}$-hyperexcentric modules for Lie algebras

Donald W. Barnes
  1 Little Wonga Rd.
  Cremorne NSW 2090

Let $\mathfrak{F}$ be a saturated formation of soluble Lie algebras over the field $F$, and let $L \in \mathfrak{F}$. Let $V$ and $W$ be $\mathfrak{F}$-hypercentral and $\mathfrak{F}$-hyperexcentric $L$-modules respectively. Then $V \otimes_F W$ and $\operatorname{Hom}_F(V, W)$ are $\mathfrak{F}$-hyperexcentric and $H^n(L, W) = 0$ for all $n$.
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