Let Q be a finite acyclic quiver and Rep (Q, R) be the category of representations of Q with
values in category of R-modules. It is shown that a representation X∈ Rep (Q, R) is a …

Given a field k, a finite-dimensional k-algebra A, and a finite acyclic quiver Q, let AQ be the
path algebra of Q over A. Then the category of representations of Q over A is equivalent to …

Given a unitary artinian ring R and a finite acyclic quiver Q, let Λ:= RQ be the path ring of Q
over R. Then Gorenstein-projective Λ-modules are exactly the separated monic …

For a quiver Q, ak-algebra A, and an additive full subcategory 𝒳 of A-mod, the
monomorphism category Mon (Q, 𝒳) is introduced. The main result says that if T is an A …

We study total acyclicity for complexes of projective and injective representations of quivers.
A classification is given for such complexes in terms of associated vertex-complexes. When …

Let Rep (Q, R) be the category of representations of R-modules over the linear quiver $
Q=(\bullet\rightarrow\bullet\rightarrow\cdots\rightarrow\bullet) $. It is mainly studied and …

Let R be a ring and 𝒬 be a finite quiver. We give an explicit formula for the injective
envelopes and projective precovers in the category Rep (𝒬 I, R) of bound representations of …

For $\Lambda $ a selfinjective algebra, and $ Q $ a finite quiver without oriented cycles, the
algebra $\Lambda Q $ is a Gorenstein algebra and the category ${\rm Gproj}\Lambda Q $ of …

We study Gorenstein flat objects in the category Rep (Q, R) of representations of a left rooted
quiver Q with values in Mod (R), the category of all left R-modules, where R is an arbitrary …

Let $ Q $ be a quiver and $ R $ an associative ring. A representation by $ R $-modules of $
Q $ is called strongly fp-injective if it admits a pure acyclic injective resolution in the category …