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This paper is devoted to morphisms killing weights in a range (as defined by the first author) and to objects without these weights (as essentially defined by J. Wildeshaus) in a triangulated category endowed with a weight structure . We describe several new criteria for morphisms and objects to be of these types. In some of them we use virtual -truncations and a -structure adjacent to . In the case where the latter exists, we prove that a morphism kills weights if and only if it factors through an object without these weights; we also construct new families of torsion theories and projective and injective classes. As a consequence, we obtain some "weakly functorial decompositions" of spectra (in the stable homotopy category ) and a new description of those morphisms that act trivially on the singular cohomology with coefficients in an arbitrary abelian group . [ABSTRACT FROM AUTHOR]

Intervals and hearts of intervals in the lattice of torsion parts for an abelian category are closely related to various concepts such as wide subcategory, ICE-closed subcategory, and tilting theory. On the other hand, in order to characterize the Melkersson condition suitable for local cohomology theory, we introduced the concept of torsion theory connected by a Serre subcategory in the category of modules. The paper shows that these seemingly unrelated concepts occur simultaneously in the larger context called the torsion theory connected by a heart. [ABSTRACT FROM AUTHOR]

For a commutative, unital and integral quantale V, we generalize to V-groups the results developed by Gran and Michel for preordered groups. We first of all show that, in the category V- Grp of V-groups, there exists a torsion theory whose torsion and torsion-free subcategories are given by those of indiscrete and separated V-groups, respectively. It turns out that this torsion theory induces a monotone-light factorization system that we characterize, and it is then possible to describe the coverings in V- Grp . We next classify these coverings as internal actions of a Galois groupoid. Finally, we observe that the subcategory of separated V-groups is also a torsion-free subcategory for a pretorsion theory whose torsion subcategory is the one of symmetric V-groups. As recently proved by Clementino and Montoli, this latter category is actually not only coreflective, as it is the case for any torsion subcategory, but also reflective. [ABSTRACT FROM AUTHOR]

This paper is dedicated to the study of smashing weight structures (these are the weight structures "coherent with coproducts"), and the application of their properties to t-structures. In particular, we prove that the hearts of compactly generated t-structures are Grothendieck abelian categories; this statement strengthens earlier results of several other authors. The central theorem of the paper is as follows: any perfect (as defined by Neeman) set of objects of a triangulated category generates a weight structure; we say that weight structures obtained this way are perfectly generated. An important family of perfectly generated weight structures are (the opposites to) the ones right adjacent to compactly generated t-structures; they give injective cogenerators for the hearts of the latter. Moreover, we establish the following not so explicit result: any smashing weight structure on a well generated triangulated category (this is a generalization of the notion of a compactly generated category that was also defined by Neeman) is perfectly generated; actually, we prove more than that. Furthermore, we give a classification of compactly generated torsion theories (these generalize both weight structures and t-structures) that extends the corresponding result of D. Pospisil and J. Šťovíček to arbitrary smashing triangulated categories. This gives a generalization of a t-structure statement due to B. Keller and P. Nicolas. [ABSTRACT FROM AUTHOR]

Tilting theory plays an important role in the representation theory of coalgebras. This paper seeks how to apply the theory of localization and colocalization to tilting torsion theory in the category of comodules. In order to better understand the process, we give the (co)localization for morphisms, (pre)covers and special precovers. For that reason, we investigate the (co)localization in tilting torsion theory for coalgebras. [ABSTRACT FROM AUTHOR]

The shear modulus of pulp fibers is difficult to measure and only very little literature is available on this topic. In this work we are introducing a method to measure this fiber property utilizing a custom built instrument. From the geometry of the fiber cross section, the fiber twisting angle and the applied torque, the shear modulus is derived by de Saint Venant's theory of torsion. The deformation of the fiber is applied by a moving coil mechanism. The support of the rotating part consists of taut bands, making it nearly frictionless, which allows easy control of the torque to twist the fiber. A permanent magnet moving coil meter was fitted with a sample holder for fibers and torque references. Measurements on fine metal bands were performed to validate the instrument. The irregular shape of the fibers was reconstructed from several microtome cuts and an apparent torsion constant was computed by applying de Saint Venant's torsion theory. Fibers from two types of industrial pulp were measured: thermomechanical pulp (TMP) and Kraft pulp. The average shear modulus was determined as (2.13 ± 0.36) GPa for TMP and (2.51 ± 0.50) GPa for Kraft fibers, respectively. The TMP fibers showed a smaller shear modulus but, due to their less collapsed state, a higher torsional rigidity than the kraft fibers. [ABSTRACT FROM AUTHOR]

We explore a non-abelian torsion theory in the category of preordered groups: the objects of its torsion-free subcategory are the partially ordered groups, whereas the objects of the torsion subcategory are groups (with the total order). The reflector from the category of preordered groups to this torsion-free subcategory has stable units, and we prove that it induces a monotone-light factorization system. We describe the coverings relative to the Galois structure naturally associated with this reflector, and explain how these coverings can be classified as internal actions of a Galois groupoid. Finally, we prove that in the category of preordered groups there is also a pretorsion theory, whose torsion subcategory can be identified with a category of internal groups. This latter is precisely the subcategory of protomodular objects in the category of preordered groups, as recently discovered by Clementino, Martins-Ferreira, and Montoli. [ABSTRACT FROM AUTHOR]

Using congruences, a Hoehnke radical can be defined for graphs in the same way as for universal algebras. This leads in a natural way to the connectednesses and disconnectednesses (= radical and semisimple classes) of graphs. It thus makes sense to talk about ideal-hereditary Hoehnke radicals for graphs (= hereditary torsion theories). All such radicals for the category of undirected graphs which allow loops are explicitly determined. Moreover, in contrast to what is the case for the well-known algebraic categories, it is shown here that such radicals for graphs need not be Kurosh–Amitsur radicals. [ABSTRACT FROM AUTHOR]

We show that in the category of preordered sets there is a natural notion of pretorsion theory, in which the partially ordered sets are the torsion-free objects and the sets endowed with an equivalence relation are the torsion objects. Correspondingly, it is possible to construct a stable category factoring out the objects that are both torsion and torsion-free. [ABSTRACT FROM AUTHOR]

We consider a generalization of the notion of torsion theory, which is associated with a Serre subcategory over a commutative Noetherian ring. In 2008 Aghapournahr and Melkersson investigated the question of when local cohomology modules belong to a Serre subcategory of the module category. In their study, the notion of Melkersson condition was defined as a suitable condition in local cohomology theory. One of our purposes in this paper is to show how naturally the concept of Melkersson condition appears in the context of torsion theories. [ABSTRACT FROM AUTHOR]

All groups considered are Abelian. As is well known, in a divisible group every subgroup is essential in a direct summand. Moreover, the fully invariant subgroups play a crucial role in the structure of an Abelian group. Thus it is natural to consider the class of groups in which every fully invariant subgroup is essential in a direct summand. In this paper, we provide a construction for imbedding a torsion group into a FI-extending group in some "minimal" way. This imbedding preserves p-height. [ABSTRACT FROM AUTHOR]

A Galois connection between functorial topologies on abelian groups and subclasses of abelian groups is constructed by means of the notion of indiscrete topology. It is shown that the composition of this Galois connection with a previously introduced one coincides with the classical Galois connection induced by the notion of constant morphism. Examples are provided. [ABSTRACT FROM AUTHOR]

In this paper, which is a continuation of our previous paper [T. Albu, M. Iosif, A. Tercan, The conditions ( C) in modular lattices, and applications, J. Algebra Appl. 15 (2016), http: dx.doi.org/10.1142/S0219498816500018], we investigate the latticial counterparts of some results about modules satisfying the conditions ( C) or ( C). Applications are given to Grothendieck categories and module categories equipped with hereditary torsion theories. [ABSTRACT FROM AUTHOR]

The purpose of this article is to prove that the category of cocommutative Hopf K-algebras, over a field K of characteristic zero, is a semi-abelian category. Moreover, we show that this category is action representable, and that it contains a torsion theory whose torsion-free and torsion parts are given by the category of groups and by the category of Lie K-algebras, respectively. [ABSTRACT FROM AUTHOR]

We characterize t-structures in stable ∞-categories as suitable quasicategorical factorization systems. More precisely we show that a t-structure 픱 on a stable ∞-category C is equivalent to a normal torsion theory 픽 on C, i.e. to a factorization system 픽 = (퓔, ℳ) where both classes satisfy the 3-for-2 cancellation property, and a certain compatibility with pullbacks/pushouts. [ABSTRACT FROM AUTHOR]

We construct infinite families of pairwise non-isomorphic indecomposable totally reflexive modules of high multiplicity. Under suitable conditions on the totally reflexive modules M and N, we find infinitely many non-isomorphic indecomposable modules arising as extensions of M by N. The construction uses the bimodule structure of ${Ext^{1}_{R}}((M,N)$ over the endomorphism rings of N and M. Our results compare with a recent theorem of Celikbas, Gheibi and Takahashi, and broaden the scope of that theorem. [ABSTRACT FROM AUTHOR]

We first characterize τ-complemented modules with relative (pre)covers. We also introduce an extending module relative to τ-pure submodules on a hereditary torsion theory τ and give its relationship with τ-complemented modules. [ABSTRACT FROM AUTHOR]

We give a method to study the finiteness of the coradical filtration of a coalgebra; as a consequence, we show that a left semiartinian profinite algebra has nilpotent Jacobson radical and is right semiartinian too. Equivalently, we show that a for a semilocal profinite algebra, T-nilpotence implies nilpotence for the Jacobson radical. This answers two open questions from Iovanov et al. (J Algebra 320(5):2144-2155, ). [ABSTRACT FROM AUTHOR]

Bezrukavnikov, later together with Arinkin, recovered Deligne's work defining perverse t-structures in the derived category of coherent sheaves on a projective scheme. We prove that these t-structures can be obtained through tilting with respect to torsion theories, as in the work of Happel, Reiten and Smalø. This approach allows us to define, in the quasi-coherent setting, similar perverse t-structures for certain noncommutative projective planes. [ABSTRACT FROM AUTHOR]