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Let $A$ be a finite dimensional algebra with finite global dimension g and Loewy length l and dimension of the Jacobson radical being r. Do we have $g \leq r-(l-2)$ ?

$g \leq r$ was proven in http://www.ams.org/journals/proc/1990-108-03/S0002-9939-1990-1031675-8/S0002-9939-1990-1031675-8.pdf for monomial algebras.

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    $\begingroup$ This is an interesting, but hard, problem. To add some context, Schofield (Bull. London Math. Soc. 17 (1985), no. 4, 393-394) has shown that there is a function $f$ such that $g \leq f(\dim A)$. But I do not even know if $g \leq \dim A$ is true in general. $\endgroup$
    – Alex Dugas
    Apr 7, 2018 at 0:07

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