Torsion and torsion-free classes from objects of finite type in Grothendieck categories

Torsion Classes of Finite Type and Spectra

Given a commutative ring R (respectively a positively graded commutative ring A = ⊕j>0Aj which is finitely generated as an A0-algebra), a bijection between the torsion classes of finite type in ModR (respectively tensor torsion classes of finite type in QGrA) and the set of all subsets Y ⊆ Spec R (respectively Y ⊆ Proj A) of the form Y = S i∈Ω Yi, with Spec R \ Yi (respectively Proj A \ Yi) qua...

Torsion Pairs in Triangulated Categories

We study the properties of torsion pairs in triangulated category by introducing the notions of d-Ext-projectivity and d-Ext-injectivity. In terms of -mutation of torsion pairs, we investigate the properties of torsion pairs in triangulated category C D    U Z D Z D

Chain conditions in modular lattices with applications to Grothendieck categories and torsion theories

-torsion free Acts Over Monoids

In this paper firt of all we introduce a generalization of torsion freeness of acts over monoids, called -torsion freeness. Then in section 1 of results we give some general properties and in sections 2, 3 and 4 we give a characterization of monoids for which this property of their right Rees factor, cyclic and acts in general  implies some other properties, respectively.

Minimal Inclusions of Torsion Classes

Let Λ be a finite-dimensional associative algebra. The torsion classes of mod Λ form a lattice under containment, denoted by tors Λ. In this paper, we characterize the cover relations in tors Λ by certain indecomposable modules. We consider three applications: First, we show that the completely join-irreducible torsion classes (torsion classes which cover precisely one element) are in bijection...