This article is cited in 4 papers

RESEARCH ARTICLE

Preradicals and characteristic submodules: connections and operations

A. I. Kashu

Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, 5 Academiei str. Chişinău, MD-2028 Moldova

Abstract: For an arbitrary module $M\in R$-Mod the relation between the lattice $L^{ch}(_{R}M)$ of characteristic (fully invariant) submodules of $M$ and big lattice $R$-pr of preradicals of $R$-Mod is studied. Some isomorphic images of $L^{ch}(_{R}M)$ in $R$-pr are constructed. Using the product and coproduct in $R$-pr four operations in the lattice $L^{ch}(_{R}M)$ are defined. Some properties of these operations are shown and their relations with the lattice operations in $L^{ch}(_{R}M)$ are investigated. As application the case $_{R}M=_{R}R$ is mentioned, when $L^{ch}(_{R}R)$ is the lattice of two-sided ideals of ring $R$.

Keywords: preradical, lattice, characteristic submodule, product (coproduct) of preradicals.

MSC: 16D90, 16S90, 06B23

Received: 22.04.2010
Revised: 11.08.2010

Language: English

Bibliographic databases:

• 
•