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On semiprimary rings of finite global dimension

Manuel Saorin
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Abstract

Suppose that $A$ is a semiprimary ring satisfying one of the two conditions: 1) its Yoneda ring is generated in finite degrees; 2) its Loewy length is less or equal than three. We prove that the global dimension of $A$ is finite if, and only if, there is a $m>0$ such that $Ext_A^n(S,S)=0$, for all simple $A$-modules $S$ and all $n\geq m$.

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Manuel Saorin. 2003-06-02. On semiprimary rings of finite global dimension. https://arxiv.org/abs/math/0306043

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