Geodesic
Preradicals and characteristic submodules: connections and operations
Algebra and discrete mathematics, Tome 9 (2010) no. 2, pp. 61-77.

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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. 
@article{ADM_2010_9_2_a4,
     author = {A. I. Kashu},
     title = {Preradicals and characteristic submodules: connections and operations},
     journal = {Algebra and discrete mathematics},
     pages = {61--77},
     publisher = {mathdoc},
     volume = {9},
     number = {2},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2010_9_2_a4/}
}
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A. I. Kashu. Preradicals and characteristic submodules: connections and operations. Algebra and discrete mathematics, Tome 9 (2010) no. 2, pp. 61-77. http://geodesic.mathdoc.fr/item/ADM_2010_9_2_a4/