Related papers: Tilting modules arising from ring epimorphisms

We extend a classical fact about deformations of groups of units of commutative rings to $\mathbb{E}_{\infty}$-ring spectra, and we use this result to provide a map of spectra generalizing the ordinary logarithmic derivative induced by an…

Surjective homological epimorphisms with stratifying kernel can be used to construct recollements of derived module categories. These `stratifying' recollements are derived from recollements of module categories. Can every recollement be…

We introduce the notions of t-lifting modules and t-dual Baer modules, which are generalizations of lifting modules. It is shown that an amply supplemented module $M$ is t-lifting if and only if $M$ is t-dual Baer and a…

For any ring R we construct two triangulated categories, each admitting a functor from R-modules that sends projective and injective modules to 0. When R is a quasi-Frobenius or Gorenstein ring, these triangulated categories agree with each…

Let k be an algebraically closed field of positive characteristic, and let W be the ring of infinite Witt vectors over k. Suppose G is a finite group and B is a block of kG of infinite tame representation type. We find all finitely…

Let $R$ be a standard graded polynomial ring that is finitely generated over a field, and let $I$ be a homogenous prime ideal of $R$. Bhatt, Blickle, Lyubeznik, Singh, and Zhang examined the local cohomology of $R/I^t$, as $t$ grows…

Using cluster tilting theory, we investigate tilting objects in the stable category of vector bundles on a weighted projective line of weight type $(2, 2, 2, 2)$. More precisely, a tilting object consisting of rank-two bundles is…

Any cluster-tilted algebra is the relation extension of a tilted algebra. We present a method to, given the distribution of a cluster-tilting object in the Auslander-Reiten quiver of the cluster category, construct all tilted algebras whose…

Let R be a commutative, noetherian, local ring. Topological Q-vector spaces modelled on full subcategories of the derived category of R are constructed in order to study intersection multiplicities.

We study certain special tilting and cotilting modules for an algebra with positive dominant dimension, each of which is generated or cogenerated (and usually both) by projective-injectives. These modules have various interesting…

In the present paper we investigate reflexive modules over the endomorphism algebras of reflexive trace ideals in a one-dimensional Cohen-Macaulay local ring. The main theorem generalizes both of the results of S. Goto, N. Matsuoka, and T.…

Let $R$ be a commutative ring and $S$ a multiplicative subset of $R$. A ring $R$ is called an $S$-Matlis ring if $pd_RR_S\leq 1$. In this note, we give some new characterizations of $S$-Matlis rings in terms of $S$-strongly flat modules,…

The aim of this paper is to introduce tau-tilting theory, which completes (classical) tilting theory from the viewpoint of mutation. It is well-known in tilting theory that an almost complete tilting module for any finite dimensional…

Based upon properties of ordinal length, we introduce a new class of modules, the binary modules, and study their endomorphism ring. The nilpotent endomorphisms form a two-sided ideal, and after factoring this out, we get a commutative…

We study the categories of discrete modules for topological rings arising as the rings of operations in various kinds of topological K-theory. We prove that for these rings the discrete modules coincide with those modules which are locally…

We consider flat epimorphisms of commutative rings $R\to U$ such that, for every ideal $I\subset R$ for which $IU=U$, the quotient ring $R/I$ is semilocal of Krull dimension zero. Under these assumptions, we show that the projective…

Let $Q$ be a finite acyclic quiver and $A_Q$ the cluster algebra of $Q$. It is well-known that for each field $k$, the additive equivalence classes of support tilting $kQ$-modules correspond bijectively with the clusters of $A_Q$. The aim…

Let $R$ be an associative ring with unit. Given an $R$-module $M$, we can associate the following covariant functor from the category of $R$-algebras to the category of abelian groups: $S\mapsto M\otimes_R S$. With the corresponding notion…

The main purpose of this paper is to introduce the concept of $e^*$-topological ring. This class appears as a generalized form of the class of $\beta$-topological rings. In addition, we have discussed the relation between the concept of…

This paper generalize the idea of the authors in J. Pure Appl. Algebra 210 (2007) 437--445. Namely, we define and study a particular case of Gorenstein projective modules. We investigate some change of rings results for this new kind of…