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.

Voir la notice de l'article provenant de la source Math-Net.Ru

In the lattice L(RM) of all submodules of a module RM four operations are defined using the standard preradicals: α-product, ω-product, α-coproduct and ω-coproduct. Some properties of these operations, as well as some connections with the lattice operations of L(RM) are indicated. For characteristic submodules these operations were studied in the work [5].
@article{BASM_2011_2_a0,
     author = {A. I. Kashu},
     title = {On some operations in the lattice of submodules determined by preradicals},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {5--16},
     publisher = {mathdoc},
     number = {2},
     year = {2011},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/BASM_2011_2_a0/}
}
TY  - JOUR
AU  - A. I. Kashu
TI  - On some operations in the lattice of submodules determined by preradicals
JO  - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY  - 2011
SP  - 5
EP  - 16
IS  - 2
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/BASM_2011_2_a0/
LA  - en
ID  - BASM_2011_2_a0
ER  - 
%0 Journal Article
%A A. I. Kashu
%T On some operations in the lattice of submodules determined by preradicals
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2011
%P 5-16
%N 2
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/BASM_2011_2_a0/
%G en
%F BASM_2011_2_a0
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. https://geodesic-test.mathdoc.fr/item/BASM_2011_2_a0/

[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