Related papers: Auslander class, $\g_C$ and $C$--projective module…

We study the class of modules, called cosilting modules, which are defined as the categorical duals of silting module. Several characterizations of these modules and connections with silting modules are presented. We prove that Bazzoni…

We investigate projective covers of cyclically presented modules, characterizing the rings over which every cyclically presented module has a projective cover as the rings $R$ that are Von Neumann regular modulo their Jacobson radical…

The aim of this paper is to introduce and study a large class of $\mathfrak{g}$-module algebras which we call factorizable by generalizing the Gauss factorization of (square or rectangular) matrices. This class includes coordinate algebras…

We give a criterion for rings with $\m^3=0$ which are obtained as connected sums of two other rings to have non-trivial totally acyclic modules.

This article begins the study of irreducible maps involving finite-dimensional uniserial modules over finite-dimensional associative algebras. We work on the classification of irreducible maps between two uniserials over triangular…

Drinfeld recently suggested to replace projective modules by the flat Mittag--Leffler ones in the definition of an infinite dimensional vector bundle on a scheme $X$. Two questions arise: (1) What is the structure of the class $\mathcal D$…

Let $M$ be a finitely generated module over a free twisted commutative algebra $A$ that is finitely generated in degree one. We show that the projective dimension of $M({\bf C}^n)$ as an $A({\bf C}^n)$-module is eventually linear as a…

Let $R$ be a Noetherian ring and let $C$ be a semidualizing $R$-module. In this paper, by using the classes $ \mathcal{P}_C $ and $ \mathcal{I}_C $, we extend the notions of perfect and coperfect modules introduced by D.Rees \cite{R} and…

We obtain a partial classification of the finite groups $G$ for which the integral group ring $\mathbb{Z} G$ has projective cancellation, i.e. for which $P \oplus \mathbb{Z} G \cong Q \oplus \mathbb{Z} G$ implies $P \cong Q$ for projective…

We show that the category of discrete modules over an infinite profinite group has no non-zero projective objects and does not satisfy Ab4*. We also prove the same types of results in a generalized setting using a ring with linear topology.

In this paper, we study representations of certain string algebras, which are referred to as of affine type $\widetilde{C}$. We introduce minimal string modules and apply them to explicitly describe components of the Auslander-Reiten…

Differential modules over a commutative differential ring R which are finitely generated projective as ring modules, with differential homomorphisms, form an additive category, so their isomorphism classes form a monoid. We study the…

Let A be a connected left artinian ring with radical square zero and with n simple modules. If A is not self-injective, then we show that any module M with Ext^i(M,A) = 0 for 1 \le i \le n + 1 is projective. We also determine the structure…

In this paper, we introduce principally $\delta$-lifting modules which are analogous to $\delta$-lifting modules and principally $\delta$-semiperfect modules as a generalization of $\delta$-semiperfect modules and investigate their…

Let $\mathcal{X}$ be a class of $R$-modules. In this paper, we investigate \;$\mathcal{X}$-(f.g.)injective ((f.g.)projective) and DG-$\mathcal{X}$-injective (projective) complexes which are generalizations of injective (projective) and…

We study the so-called closed and splitting subsemimodules and submodules of a given semimodule or module, respectively. We describe lattices of subsemimodules and of closed subsemimodules and posets of splitting subsemimodules and…

In this paper, we consider finitely generated modules over commutative Noetherian rings whose tensor products have finite projective dimension. We construct examples of modules of infinite projective dimension (and also of infinite…

We give an explicit algorithm to compute a projective resolution of a module over the noncommutative ring based on the noncommutative Groebner bases theory.

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,…

We continue the program started in \cite{M1} to understand the combinatorial commutative algebra of the projective coordinate rings of the moduli stack $\mathcal{M}_{C, \vec{p}}(SL_2(\C))$ of quasi-parabolic $SL_2(\C)$ principal bundles on…