It is proved that an element $r$ in the center of a coherent ring $Lambda$ annihilates $mathrm{Ext}^{n}_{Lambda}(M,N)$, for some positive integer $n$ and all finitely presented $Lambda$-modules $M$ and $N$, if and only if the bounded derived category of $Lambda$ is an extension of the subcategory consisting of complexes annihilated by $r$ and those obtained as $n$-fold extensions of $Lambda$. This has applications to finiteness of dimension of derived categories.
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机译：证明在相干环$ Lambda $中心的元素$ r $会消灭$ mathrm {Ext} ^ {n} _ { Lambda}（M，N）$，对于某个正整数$ n $和所有有限表示的$ Lambda $-模块$ M $和$ N $，并且仅当$ Lambda $的有界派生类别是该子类别的扩展时，该子类别包括由$ r $消灭的复合物和作为$获得的复合物$ Lambda $的n $倍扩展名。这适用于派生类别的维数有限。
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