Given A an artin algebra we study when the non-zero composition of four irreducible
morphisms between indecomposable A-modules belongs to the fifth power of the radical of …

We describe in the paper the graded centers of the bounded derived categories of the
derived discrete algebras. In particular, we prove that if A is a derived discrete algebra, then …

Abstract Recently, Wang, Wei and Zhang introduced the notion of recollements of
extriangulated categories. In this paper, let (A, B, C) be a recollement of extriangulated …

We prove that the finitistic dimension conjecture, the Gorenstein Symmetry Conjecture, the
Wakamatsu-tilting conjecture and the generalized Nakayama conjecture hold for artin …

We prove that an artin algebra is of finite representation type if and only if almost all finitely
generated indecomposable-modules are cycle-finite. Moreover, we prove that every cycle …

The article compares the finitistic dimensions of two algebras involved in an idealized
extension of Artin algebras under certain conditions. Precisely, we prove that, for the …

Two artin algebras $\Lambda $ and $\Lambda'$ are said to be stably equivalent if the
categories of finitely generated modules modulo projective for $\Lambda $ and $\Lambda' …

In this paper, we investigate the resolving resolution dimension with respect to the
recollements of abelian categories. Let (𝒜, ℬ, 𝒞) be a recollement of abelian categories such …

We study Auslander-Reiten theory in proper abelian subcategories of triangulated
categories with a Serre functor. To initiate this, we use approximations of a Serre functor to …

Problems solved by using degrees of irreducible morphisms Page 188 Contemporary
Mathematics Volume 607, 2014 http://dx. doi. org/10.1090/conm/607/12077 Problems solved …