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Let H be a connected wild hereditary path algebra. We prove that if Z is a quasi-simple regular brick, and [r]Z indecomposable regular of quasi-length r and with quasi-top Z, then .
The strong global dimension of a finite dimensional algebra A is the maximum of the width of indecomposable bounded differential complexes of finite dimensional projective A-modules. We prove that the strong global dimension of a finite dimensional radical square zero algebra A over an algebraically closed field is finite if and only if A is piecewise hereditary. Moreover, we discuss results concerning the finiteness of the strong global dimension of algebras and the related problem on the density...
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