Related papers: Fp-projective periodicity

In \cite{AB}, Auslander and Bridger introduced Gorenstein projective modules and only about 40 years after their introduction a finite dimensional algebra $A$ was found in \cite{JS} where the subcategory of Gorenstein projective modules did…

A correspondence functor is a functor from the category of finite sets and correspondences to the category of $k$-modules, where $k$ is a commutative ring. We determine exactly which simple correspondence functors are projective. Moreover,…

The classes $\mathcal D _{\mathcal Q}$ of flat relative Mittag-Leffler modules are sandwiched between the class $\mathcal F \mathcal M$ of all flat (absolute) Mittag-Leffler modules, and the class $\mathcal F$ of all flat modules. Building…

A version of group cohomology for locally compact groups and Polish modules has previously been developed using a bar resolution restricted to measurable cochains. That theory was shown to enjoy analogs of most of the standard algebraic…

We consider the natural generalization of the notion of the order of a phantom map from the topological setting to triangulated categories. When applied to the derived category of the category of countable flat modules over a countable…

We provide various ways to characterise $\Sigma$-pure-injective objects in a compactly generated triangulated category. These characterisations mimic analogous well-known results from the model theory of modules. The proof involves two…

Let $(S, \n)$ be a commutative noetherian local ring and $\omega\in\n$ be non-zerodivisor. This paper deals with the behavior of the category $\mon(\omega, \cp)$ consisting of all monomorphisms between finitely generated projective…

In this paper the authors produce a projective indecomposable module for the Frobenius kernel of a simple algebraic group in characteristic $p$ that is not the restriction of an indecomposable tilting module. This yields a counterexample to…

Assume that $R$ is a non-right perfect ring. Then there is a proper class of classes of (right $R$-) modules closed under transfinite extensions lying between the classes $\mathcal P _0$ of projective modules, and $\mathcal F _0$ of flat…

It is now very known how the subprojectivity of modules provides a fruitful new unified framework of the classical projectivity and flatness. In this paper, we extend this fact to the category of complexes by generalizing and unifying…

Motivated by the relation between Schur algebra and the group algebra of a symmetric group, along with other similar examples in algebraic Lie theory, Min Fang and Steffen Koenig addressed some behaviour of the endomorphism algebra of a…

In this paper we prove a recent conjecture by M. Hirsch, which says that if $(f,\Omega)$ is a discrete time monotone dynamical system, with $f\colon \Omega\to\Omega$ a homeomorphism on an open connected subset of a finite dimensional vector…

In this paper, we examine the class of cofibrant modules over a group algebra $kG$, that were defined by Benson in [2]. We show that this class is always the left-hand side of a complete hereditary cotorsion pair in the category of…

Let $T_R(M)$ be a tensor ring and $\mathcal{X}$, $\mathcal{Y}$ be two classes of $R$-modules. Under certain conditions, we prove that a $T_R(M)$-module $(A, u)$ is $Ind(\mathcal{X})$-Gorenstein projective if and only if $u$ is monomorphic…

Suppose that $(\mathcal{F},\mathcal{M})$ is an injective structure of $R$-Mod such that the class $\mathcal{F}$ is closed for direct limits, then two modules in $\mathcal{M}$ are isomorphic if there are maps in $\mathcal{F}$ from each one…

Recently, several authors have adopted new alternative approaches in the study of some classical notions of modules. Among them, we find the notion of subprojectivity which was introduced to measure in a way the degree of projectivity of…

We prove that the projective unit group $\mathrm{PGL}(R)$, i.e., the quotient of the unit group $\mathrm{GL}(R)$ modulo its center, of any non-discrete irreducible, continuous ring $R$ is simple. Moreover, we show that $\mathrm{GL}(R)$ has…

Let $(\mathcal{A,B})$ be a complete and hereditary cotorsion pair in the category of left $R$-modules. In this paper, the so-called Gorenstein projective complexes respect to the cotorsion pair $(\mathcal{A}, \mathcal{B})$ are introduced.…

We study thick subcategories of the category of 2-term complexes of projective modules over an associative algebra. We show that those thick subcategories that have enough injectives are in explicit bijection with 2-term silting complexes…

For an eventually periodic module, we have the degree and the period of its first periodic syzygy. This paper studies the former under the name \lq\lq periodic dimension\rq\rq. We give a bound for the periodic dimension of an eventually…