Institutul de Matematică şi Informatică "Vladimir Andrunachievici"
Universitatea de Stat din MoldovaRO EN
The classes of divisible and reduced modules associated to the torsion theories. (English)
Authors: Caşu Alexei
Abstract
To every torsion $r$ of category $R$-Mod two classes of modules of Mod-$R$ are associated: the class $D_r$ of $r$-divisible modules and the class $\Cal R_r$ of $r$-reduced modules [1]. These notions are generalized for idempotent radicals of $R$-Mod and the relations between the classes $\Cal T_r$, $\Cal F_r$, $\Cal D_r$ and $\Cal R_r$ are shown. The inverse transition from the classes $\Cal L \subseteq$ Mod-$R$ to the idempotent radicals of $R$-Mod is studied. In the case of torsion this transition is modified and some applications to the Morita contexts are considered.Institutul de Matematică şi Informatică
Academia de Ştiinţe a Moldovei
str. Academiei 5, MD-2028 Chişinău, Moldova
Academia de Ştiinţe a Moldovei
str. Academiei 5, MD-2028 Chişinău, Moldova
Contents
- To the 35th anniversary of the Institute of Mathematics and Computer Science of the Academy of Sciences of the Republic of Moldova.
- On coverings in the lattice of linear topologies. (English)
- Radical assignments and radical classes. (English)
- On rings with a distributive lattice of pretorsions. (Russian)
- On product-closed radical classes of abelian groups. (English)
- Some remarks concerning nuclei on semiring. (English)
- The classes of divisible and reduced modules associated to the torsion theories. (English)
- Zero divisors in group-based algebras. Algebras without zero divisors. (English)
- Category of representations of elementary knowledge. (English)
- On endomorphism rimgs without nonzero nilpotent elements. II. (English)
- On the intersection of radical classes. (English)
- Vladimir Ivanovich Arnautov. A tribute in honor of his 60th birthday.
