Wydawnictwa / Czasopisma IMPAN / Colloquium Mathematicum / Wszystkie zeszyty

Streszczenie

We study the global cohomological width of artin algebras. Using the construction of indecomposable objects in the triangulated category via taking cones due to Happel and Zacharia (2008), we establish that global cohomological width coincides with strong global dimension. Moreover, an upper bound for the global cohomological width of piecewise hereditary algebras is obtained. As an application, we construct finite-dimensional piecewise hereditary algebras of type $\mathbb {A}$ and $\mathbb {D}$ with global cohomological width an arbitrary positive integer $m$. Finally, we find a relation between recollements and global cohomological width.