On semiprimary rings of finite global dimension

Details On semiprimary rings of finite global dimension On semiprimary rings of finite global dimension

2003-06-02

arxiv.org/abs/math/0306043v1

Mathematics

Rings and Algebras

Scientific paper

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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