Given a finite dimensional algebra A over a field k, and a finite acyclic quiver Q, let Λ= A⊗ kk
Q/I, where kQ is the path algebra of Q over k and I is a monomial ideal. This paper is devoted …

For a finite acyclic quiver Q, an ideal I of a path algebra kQ generated by monomial relations,
and a finite-dimensional k-algebra A, we introduce the separated monic representations of a …

Let R be any associative ring, na positive integer and X a full subcategory of the category of
R-modules. The monomorphism category S n (X) of X consists of all the objects (X i, φ i) …

Motivated by some properties satisfied by Gorenstein projective and Gorenstein injective
modules over an Iwanaga-Gorenstein ring, we present the concept of left and right n …

We study homological behavior of modules satisfying the Auslander condition. Assume that
AC is the class of left R-modules satisfying the Auslander condition. It is proved that each …

For a $ k $-algebra $ A $, a quiver $ Q $, and an ideal $ I $ of $ kQ $ generated by monomial
relations, let $\Lambda:= A\otimes_k kQ/I $. We introduce the monic representations of $(Q …

Let 𝒟 be either the category of R-modules or the category of chain complexes of R-modules
and ℳ a cofibrantly generated hereditary abelian model structure on 𝒟. First, we get a new …

In this paper, we study the pair (GP(R),GP(R)^⊥) where GP(R) is the class of all Gorenstein
projective modules. We prove that it is a complete hereditary cotorsion theory, provided …

We introduce a generalization of the Gorenstein injective modules: the Gorenstein FP n-
injective modules (denoted by GI n). They are the cycles of the exact complexes of injective …

Given a non-negative integer n and a complete hereditary cotorsion triple, the notion of
subcategories in an abelian category is introduced. It is proved that a virtually Gorenstein …