Related papers: Arf rings, simple singularities and reflexive modu…

Let (R,m) be a Noetherian local ring of depth d and C a semidualizing R-complex. Let M be a finite R-module and t an integer between 0 and d. If G_C-dimension of M/IM is finite for all ideals I generated by an R-regular sequence of length…

Let $R$ be a commutative ring and $\Gamma$ a commutative monoid of finite type. We study algebraic properties of modules and derivations over the associated ring $\mathcal F(\Gamma,R)$ of Dirichlet convolutions. If $\Gamma$ is cancellative…

There are several theorems describing the intricate relationship between flatness and associated primes over commutative Noetherian rings. However, associated primes are known to act badly over non-Noetherian rings, so one needs a suitable…

In this paper we consider reduced (non-normal) commutative noetherian rings $R$. With the help of conductor ideals and trace ideals of certain $R$-modules we deduce a criterion for a reflexive $R$-module to be closed under multiplication…

Let $A$ be an Iwanaga-Gorenstein ring. Enomoto conjectured that a self-orthogonal $A$-module has finite projective dimension. We prove this conjecture for $A$ having the property that every indecomposable non-projective maximal…

Let $R$ be a commutative noetherian ring, $I,J$ be two ideals of $R$, $M$ be an $R$-module, and $\mathcal{S}$ be a Serre class of $R$-modules. A positive answer to the Huneke$^,$s conjecture is given for a noetherian ring $R$ and minimax…

Let $R$ be a domain of Krull dimension one, we study when the class $\mathcal{F}$ of modules over $R$ that are arbitrary direct sums of finitely generated torsion-free modules is closed under direct summands. If $R$ is local, we show that…

In this paper we present a systematic study of the reflexivity properties of homologically finite complexes with respect to semidualizing complexes in the setting of nonlocal rings. One primary focus is the descent of these properties over…

Matlis showed that the injective hull of a simple module over a commutative Noetherian ring is Artinian. Many non-commutative Noetherian rings whose injective hulls of simple modules are locally Artinian have been extensively studied…

Thirty years ago, Huneke (for local rings) and Lyubeznik (in general) conjectured that for all regular rings $R$, the local cohomology modules $H^i_I(R)$ have finitely many associated prime ideals. We prove substantial new cases of their…

Let R be a commutative ring with identity. We investigate some ring-theoretic properties of weakly Laskerian R-modules. Our results indicate that weakly Laskerian rings behave as Noetherian ones in many respects. However, we provide some…

Let $\k$ be an algebraically closed field, let $\A$ be a finite dimensional $\k$-algebra and let $V$ be a $\A$-module with stable endomorphism ring isomorphic to $\k$. If $\A$ is self-injective then $V$ has a universal deformation ring…

In this note we study dual coalgebras of algebras over arbitrary (noetherian) commutative rings. We present and study a generalized notion of coreflexive comodules and use the results obtained for them to characterize the so called…

In this paper, we characterize several properties of commutative notherian local rings in terms of the left perpendicular category of the category of finitely generated modules of finite projective dimension. As an application we prove that…

Let $(R, \mathfrak{m})$ be a Noetherian local ring. In this paper, we introduce a dual notion for dualizing modules, namely codualizing modules. We study the basic properties of codualizing modules and use them to establish an equivalence…

Let $A$ be a commutative arithmetical ring. The ring $A$ has Krull dimension if and only if every factor ring of $A$ is finite-dimensional and does not have idempotent proper essential ideals. The study is supported by Russian Science…

Let $R$ be a commutative $F$-algebra, where $F$ is a field of characteristic 0, satisfying the following conditions: $R$ is equidimensional of dimension $n$, every residual field with respect to a maximal ideal is an algebraic extension of…

Different and distinct notions of regularity for modules exist in the literature. When these notions are restricted to commutative rings, they all coincide with the well-known von-Neumann regularity for rings. We give new characterizations…

We study homological properties of test modules that are, in principle, modules that detect finite homological dimensions. The main outcome of our results is a generalization of a classical theorem of Auslander and Bridger: we prove that,…

We characterise Dedekind rings among not necessarily Noetherian domains by a property of their module homomorphisms. Our proof relies on a homological algebra argument.