IMCS/Publications/BASM/Issues/BASM n.2 (30), 1999/

The classes of divisible and reduced modules associated to the torsion theories. (English)

Authors: Caşu Alexei


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