Related papers: A criterion for dualizing modules

Let $C$ be a semidualizing module. We first investigate the properties of finitely generated $G_C$-projective modules. Then, relative to $C$, we introduce and study the rings of Gorenstein (weak) global dimensions at most 1, which we call…

We construct the Cartier duality equivalence for affine commutative group schemes $G$ whose coordinate ring is a flat Mittag-Leffler module over an arbitrary base ring $R$. The dual $G^\vee$ of $G$ turns out to be an ind-finite ind-scheme…

The main goal of this paper is to characterize rings over which the mininjective modules are injective, so that the classes of mininjective modules and injective modules coincide. We show that these rings are precisely those Noetherian…

It is shown that any left module A over a ring R can be written as the intersection of a downward directed system of injective submodules of an injective module; equivalently, as an inverse limit of one-to-one homomorphisms of injectives.…

Let $(R,\fm)$ be a Cohen-Macaulay local ring. If $R$ has a canonical module, then there are some interesting results about duality for this situation. In this paper, we show that one can indeed obtain similar these results in the case $R$…

Let $R$ be a commutative noetherian ring, and let $C$ be a semidualizing $R$-module. In this paper, we study levels of bounded complexes of finitely generated $R$-modules with respect to the full subcategory $\mathsf{G}_{C}(R)$ consisting…

We study the module categories of a tilted algebra C and the corresponding cluster-tilted algebra B. We investigate how various properties of a C-module are affected when considered in the module category of B. We give a complete…

Examples are given to show that the support of a complex of modules over a commutative noetherian ring may not be read off the minimal semi-injective resolution of the complex. The same examples also show that a localization of a…

Let $R$ be a commutative ring. An $R$-module $M$ is called a semi-regular $w$-flat module if $\Tor_1^R(R/I,M)$ is $\GV$-torsion for any finitely generated semi-regular ideal $I$. In this article, we show that the class of semi-regular…

Let $R$ be a commutative unital ring and $N$ be a submodule of an $R$-module $M$. The submodule $\langle E_M(N)\rangle$ generated by the envelope $E_M(N)$ of $N$ is instrumental in studying rings and modules that satisfy the radical…

Let $R$ be a left and right Noetherian ring. We introduce the notion of the torsionfree dimension of finitely generated $R$-modules. For any $n\geq 0$, we prove that $R$ is a Gorenstein ring with self-injective dimension at most $n$ if and…

Let $R$ be a $G$ graded commutative ring and $M$ be a $G$-graded $R$-module. The set of all graded second submodules of $M$ is denoted by $Spec_G^s(M)$ and it is called the graded second spectrum of $M$. In this paper, we discuss graded…

In this note, finite modules locally of finite injective dimension over commutative Noetherian rings are characterized in terms of vanishing of Ext modules.

Let R be a commutative ring with identity and S be a multiplicatively closed subset of R. The aim of this paper is to introduce the notion of fully S-idempotent modules as a generalization of fully idempotent modules and investigate some…

Both the classes of $R$-coneat injective modules and its superclass, pure Baer injective modules, are shown to be preenveloping. The former class is contained in another one, namely, self coneat injectives, i.e. modules $M$ for which every…

Let $R$ be a commutative Noetherian ring, and let $N$ be a non-zero finitely generated $R$-module. The purpose of this paper is to show that $N$ is locally unmixed if and only if, for any $N$-proper ideal $I$ of $R$ generated by $\Ht_N I$…

Let $R$ denote a Noetherian ring and an ideal $J \subset R$ with $U = \operatorname{Spec R} \setminus V(J)$. For an $R$-module $M$ there is an isomorphism $\Gamma(U, \tilde{M}) \cong \varinjlim \operatorname{Hom}_R(J^n,M)$ known as…

The notion of cosilting module was recently introduced as a generalization of the notion of cotilting module. In this paper, we give a characterization of (partial) cosilting modules in terms of two-term cosilting complexes. Moreover, we…

We count the number of submodules of an arbitrary module over a countable noetherian commutative ring. We give, along the way, a structural description of meager modules, which are defined as those that do not have the square of a simple…

Let $R$ be a commutative ring with identity and $M$ a unitary $R$-module. The purpose of this paper is to introduce the concept of semi-$n$-submodules as an extension of semi $n$-ideals and $n$-submodules. A proper submodule $N$ of $M$ is…