On the Dimensions of Path Algebras
In this paper we study the representation dimension as well as the derived dimension of the path algebra of an artin algebra over a finite and acyclic quiver.
math.RT↗
arXiv subjects
Javad Asadollahi
Publications and source records attributed to Javad Asadollahi.
On the derived dimension of abelian categories
We give an upper bound on the dimension of the bounded derived category of an abelian category. We show that if $\CX$ is a sufficiently nice subcategory of an abelian category, then derived dimension of $\CA$ is at most $\CX$-dim$\CA$, provided $\CX$-dim$\CA$ is greater than one. We provide some applications.
math.RT↗
An analogue of a theorem due to Levin and Vasconcelos
Let $(R,\m)$ be a Noetherian local ring. Consider the notion of homological dimension of a module, denoted H-dim, for H= Reg, CI, CI$_*$, G, G$^*$ or CM. We prove that, if for a finite $R$-module $M$ of positive depth, $\Hd_R({\m}^iM)$ is finite for some $i \geq \reg(M)$, then the ring $R$ has property H.
math.AC↗