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...

Let R be a split extension of an artin algebra A by a nilpotent bimodule ${}_A{Q}_A$, and let M be an indecomposable non-projective A-module. We show that the almost split sequences ending with M in mod A and mod R coincide if and only if $Ho{m}_A(Q,{\tau }_{A}M)$ = 0 and $M{\otimes }_{A}Q=0$.

We study associative, basic n × n𝔸-full matrix algebras over a field, whose multiplications are determined by structure systems 𝔸, that is, n-tuples of n × n matrices with certain properties.