RO EN
Torsion theories and subcategories of divisible modules. (English)
Authors: Caşu Alexei
Abstract
We study the Morita context $(R$, \ ${}_RU_S$, \ ${}_SV_R$, \ $S)$ with trase - ideals $I=(U,V)\triangleleft R$ and $J=[V,U]\triangleleft S$. It is well known that $\Cal L_I(R~-~Mod)\cong$$\Cal L_J(S~-~Mod)$, where $\Cal L_I(R~-~Mod)$ is the lattice of all torsion theories of $R-Mod$ with Gabriel topologies containing $I$. To every torsion teory $r\in \Cal L(R-Mod)$ the subcategory $\Cal D(r)\subseteq Mod-R$ of all $r$-divisible modules is associated. We prove that the mentioned isomorphism implies a bijection between subcategories $\Cal D(r)$ \ $(r\ge r_{_I})$ of divisible modules of $Mod-R$ and subcategories $\Cal D(r^\prime)$ $(r^\prime \ge r_{_J})$ of divisible modules of $Mod-S$.Institutul de Matematică Academia de Ştiinţe a Moldovei
str. Academiei 5, MD-2028 Chişinău, Moldova
str. Academiei 5, MD-2028 Chişinău, Moldova
Contents
- Approximate solution of singular integral equations with the help of series with respect to Faber-Laurent polynomials. (Russian)
- Global attractors of infinite-dimensional dynamical systems. I. (Russian)
- β-acyclic schemes of databases. (Romanian)
- Methods of derivation of semi-minor and pseudo-minor groups of $W$-symmetry. (Russian)
- On primitive solvable permutation groups with commutative stabilizer of a point. II. (Russian)
- Finite generated subalgebras of free CHQ-algebra. (English)
- Submodules determined by cohereditary radicals. (English)
- On strongly regular near-rings. (English)
- Impact of viscoelastic rod upon an obstacle. (Russian)
- On the property of a right ideal of a ring to be two-sided. (Russian)
- Energy saving in agro-food complex. (English)
- Impact of an elastic rod of finite length upon a compliant obstacle. II. (Russian)
- On automorphism groups of left-distributive quasigroups. (Russian)
- Torsion theories and subcategories of divisible modules. (English)
- Generating functions for comitants of differential systems. (Russian)
