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## The characteristic submodules determined by pretorsions, torsions and jansian torsions. (English)

Authors: Marcov R.

### Abstract

The submodule $N$ of module $M$ is said to be {\bf $T$-characteristic} in $M$ $(N\subseteq^TM)$ for the given type $T$ of preradicals if there exists a preradical $r$ of type $T$ such that $r(M)=N$. In this article the $T$-characteristic submodules for three types of preradicals (pretorsions, torsions, jansian torsions) are investigated. For every case the relation $N\subseteq^TM$ is characterized, some its properties are proved, all preradicals $r$ of type $T$ such that $r(M)=N$ are described. Moreover, for every module $M$ the set $I\!\!L_T(M)$ of all $T$-characteristic submodules of $M$ is transformed into a complete lattice and a set of properties of this lattice is revealed.

Institutul de Matematică Academia de Ştiinţe a Moldovei
str. Academiei 5, MD-2028 Chişinău, Moldova