Related papers: t-Dual Baer Modules and t-Lifting Modules

Given a local ring $(R, \mathfrak{m})$ and an ideal $\mathfrak{a}$ of positive height, we give a way of computing multiplier module ${J}(\omega_{{T}}, t^{-\lambda})$ for the extended Rees algebra ${T} =R[\mathfrak{a} t, t^{-1}]$ for an…

Let $R$ be a commutative Noetherian ring. It is shown that $R$ is Artinian if and only if every $R$-module is good, if and only if every $R$-module is representable. As a result, it follows that every nonzero submodule of any representable…

We study infinite dimensional tilting modules over a concealed canonical algebra of domestic or tubular type. In the domestic case, such tilting modules are constructed by using the technique of universal localization, and they can be…

We show that a differential module is Gorenstein projective if and only if its underlying module is Gorenstein projective. Dually, a differential module is Gorenstein injective if and only if its underlying module is Gorenstein injective.

In this note we show that a ring R is left perfect if and only if every left R-module is weakly supplemented if and only if R is semilocal and the radical of the countably infinite free left R-module has a weak supplement.

Connections between heaps of modules and (affine) modules over rings are explored. This leads to explicit, often constructive, descriptions of some categorical constructions and properties that are implicit in universal algebra and…

Let R be a commutative domain. We prove that an R-module B is projective if and only if Ext^1(B,T)=0 for any torsion module T. This answers in the affirmative a question raised by Kaplansky in 1962.

Baer's Criterion of injectivity implies that injectivity of a module is a factorization property w.r.t. a single monomorphism. Using the notion of a cotorsion pair, we study generalizations and dualizations of factorization properties in…

We show that the cosupport of a commutative noetherian ring is precisely the set of primes appearing in a minimal pure-injective resolution of the ring. As an application of this, we prove that every countable commutative noetherian ring…

In this article, we prove that induced modules of support $\tau$-tilting modules over blocks of finite groups satisfying inertial-invariant condition are also support $\tau$-tilting modules.

Anderson introduced t-modules as higher dimensional analogs of Drinfeld modules. Attached to such a t-module, there are its t-motive and its dual t-motive. The t-module gets the attribute "abelian" when the t-motive is a finitely generated…

We investigate the question of when free structures of infinite rank (in a variety) possess model-theoretic properties like categoricity in higher power, saturation, or universality. Concentrating on left $R$-modules we show, among other…

Every automorphism-invariant right non-singular $A$-module is injective if and only if the factor ring of the ring $A$ with respect to its right Goldie radical is a right strongly semiprime ring.

We first introduce and study the notion of semi-regular flat modules, and then show that a ring $R$ is a strong \Prufer\ ring if and only if every submodule of a semi-regular flat $R$-module is semi-regular flat, if and only if every ideal…

In this paper, we introduce the concept of graded $S$-comultiplication modules. Several results concerning graded $S$-comultiplication modules are proved. We show that $N$ is a graded $S$-second submodule of a graded $S$-comultiplication…

We introduce the new concept of silting modules. These modules generalise tilting modules over an arbitrary ring, as well as support $\tau$-tilting modules over a finite dimensional algebra recently introduced by Adachi, Iyama and Reiten.…

We study the t-structure induced by an n-tilting module T in the derived category D(R) of a ring R. Our main objective is to determine when the heart of the t-structure is a Grothendieck category. We obtain characterizations in terms of…

Let R be be a commutative ring with identity and S be a multiplicatively closed subset of R. In this article we introduce the concepts of S-coidempotent submodules and fully S-coidempotent R-modules as generalizations of coidempotent…

We extend the notion of T-duality to manifolds endowed with non-principal torus actions. The singularities of the torus action are controlled by a certain Lie algebroid, called the elliptic tangent bundle. Using this Lie algebroid, we…

Holm (H. Holm, Modules with cosupport and injective functors, Algebr. Represent. Theor., 13 (2010), 543-560) considers categories of right modules dual to those with support in a set of finitely presented modules. We extend some of his…