Geodesic
On some operations in the lattice of submodules determined by preradicals
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2011), pp. 5-16 
A. I. Kashu. On some operations in the lattice of submodules determined by preradicals. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2011), pp. 5-16. http://geodesic.mathdoc.fr/item/BASM_2011_2_a0/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In the lattice $\boldsymbol L(_RM)$ of all submodules of a module $_RM$ four operations are defined using the standard preradicals: $\alpha$-product, $\omega$-product, $\alpha$-coproduct and $\omega$-coproduct. Some properties of these operations, as well as some connections with the lattice operations of $\boldsymbol L(_RM)$ are indicated. For characteristic submodules these operations were studied in the work [5].

[1] Bican L., Kepka T., Nemec P., Rings, modules and preradicals, Marcel Dekker, New York, 1982 | MR | Zbl

[2] Raggi F., Montes J. R., Rincon H., Fernandes-Alonso R., Signoret C., “The lattice structure of preradicals”, Commun. in Algebra, 30:3 (2002), 1533–1544 | DOI | MR | Zbl

[3] Bican L., Jambor P., Kepka T., Nemec P., “Prime and coprime modules”, Fundamenta Mathematicae, 107:1 (1980), 33–45 | MR | Zbl

[4] Raggi F., Rios J., Rincon H., Fernandes-Alonso R., Signoret C., “Prime and irreducible preradicals”, J. of Algebra and its Applications, 4:4 (2005), 451–466 | DOI | MR | Zbl

[5] Kashu A. I., “Preradicals and characteristic submodules: connections and operations”, Algebra and Discrete Mathematics, 9:2 (2010), 61–77 | MR | Zbl

[6] Raggi F., Montes J. R., Wisbauer R., “Coprime preradicals and modules”, J. of Pure and Applied Algebra, 200 (2005), 51–69 | DOI | MR | Zbl