Related papers: Infinitely Generated Gorenstein Tilting Modules
We prove that a finite dimensional algebra $A$ with representation-finite subcategory consisting of modules that are semi-Gorenstein-projective and $n$-th syzygy modules is left weakly Gorenstein. This generalises a theorem of Ringel and…
This paper generalize the idea of the authors in J. Pure Appl. Algebra 210 (2007) 437--445. Namely, we define and study a particular case of Gorenstein projective modules. We investigate some change of rings results for this new kind of…
The existence of the Gorenstein projective precovers over arbitrary rings is an open question. It is known that if the ring has finite Gorenstein global dimension, then every module has a Gorenstein projective precover. We prove here a…
Let $A$ be a finite dimensional symmetric Hopf algebra over a field $k$. We show that there are $A$-modules whose Tate cohomology is not finitely generated over the Tate cohomology ring of $A$. However, we also construct $A$-modules which…
We discuss applications of exact structures and relative homological algebra to the study of invariants of multiparameter persistence modules. This paper is mostly expository, but does contain a pair of novel results. Over finite posets,…
This paper deals with some results concerning finitely generated coreduced comultiplication modules over a commutative ring.
We generalize the monomorphism category from quiver (with monomial relations) to arbitrary finite dimensional algebras by a homological definition. Given two finite dimension algebras $A$ and $B$, we use the special monomorphism category…
Relations between Gorenstein derived categories, Gorenstein defect categories and Gorenstein stable categories are established. Using these, the Gorensteinness of an algebra $A$ and invariants with respect to recollements of the bounded…
In this expository paper, we present a construction of tree modules and combine it with (infinite dimensional) tilting theory and relative Mittag-Leffler conditions in order to explore limits of the approximation theory of modules. We also…
We introduce the concept of an $n$-minimal Auslander--Gorenstein category and $n$-precluster tilting subcategory. With this, we create an analog of the higher Auslander--Solberg correspondence (arXiv:1608.04179) for exact categories. Our…
Let $\Lambda$ be an Artin algebra. In 2014, T. Adachi, O. Iyama and I. Reiten proved that the torsion funtorially finite classes in $\mathrm{mod}\,(\Lambda)$ can be described by the $\tau$-tilting theory. The aim of this paper is to…
In this note, we study commutative Noetherian local rings having finitely generated modules of finite Gorenstein injective dimension. In particular, we consider whether such rings are Cohen-Macaulay.
A recent result by J. \v{S}aroch and J. \v{S}\v{t}ov\'{\i}\v{c}ek asserts that there is a unique abelian model structure on the category of left $R$-modules, for any associative ring $R$ with identity, whose (trivially) cofibrant and…
It is well known that for Auslander algebras, the category of all (finitely generated) projective modules is an abelian category and this property of abelianness characterizes Auslander algebras by Tachikawa theorem in 1974. Let $n$ be a…
For any additive functor from modules (or, more generally, from an abelian category with enough projectives or injectives), we construct long sequences tying up together the derived functors, the satellites, and the stabilizations of the…
The principle "Every result in classical homological algebra should have a counterpart in Gorenstein homological algebra" is given in [3]. There is a remarkable body of evidence supporting this claim (cf. [2] and [3]). Perhaps one of the…
We first introduce the notion of $CM$-$\tau$-tilting free algebras as the generalization of $CM$-free algebras and show the homological properties of $CM$-$\tau$-tilting free algebras. Then we give a bijection between Gorenstein projective…
The existence of the Gorenstein projective precovers over $R$ an arbitrary ring, as well as the completeness of the Gorenstein projective cotorsion pair $(\mathcal{GP},\mathcal{GP}^{\perp})$, are open questions. In this paper, we provide…
The aim of this paper is to extend the structure theory for infinitely generated modules over tame hereditary algebras to the more general case of modules over concealed canonical algebras. Using tilting, we may assume that we deal with…
In this paper, we study the relative homological dimension based on the class of projectively coresolved Gorenstein flat modules (PGF-modules), that were introduced by Saroch and Stovicek. The resulting PGF-dimension of modules has several…