Geodesic
On the inverse operations in the class of preradicals of a module category, I
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2017), pp. 57-66 
Ion Jardan. On the inverse operations in the class of preradicals of a module category, I. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2017), pp. 57-66. http://geodesic.mathdoc.fr/item/BASM_2017_1_a5/
@article{BASM_2017_1_a5,
     author = {Ion Jardan},
     title = {On the inverse operations in the class of preradicals of a~module {category,~I}},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {57--66},
     year = {2017},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2017_1_a5/}
}
TY  - JOUR
AU  - Ion Jardan
TI  - On the inverse operations in the class of preradicals of a module category, I
JO  - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY  - 2017
SP  - 57
EP  - 66
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/BASM_2017_1_a5/
LA  - en
ID  - BASM_2017_1_a5
ER  - 
%0 Journal Article
%A Ion Jardan
%T On the inverse operations in the class of preradicals of a module category, I
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2017
%P 57-66
%N 1
%U http://geodesic.mathdoc.fr/item/BASM_2017_1_a5/
%G en
%F BASM_2017_1_a5

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

In the class $\mathbb{PR}$ of preradicals of the category of left $R$-modules $R$-Mod a new operation is defined and studied, namely the left quotient with respect to join. Some properties of this operation are shown, its compatibility with the lattice operations of $\mathbb{PR}$ (meet and join of preradicals), as well as the relations with some constructions in the “big” lattice $\mathbb{PR}$. Also some particular cases are examined.

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

[2] Golan J. S., Linear topologies on a ring, New York, Logman Sci. Techn., 1987 | MR

[3] Kashu A. I., Radicals and torsions in modules, Ştiinţa, Kishinev, 1983 (in Russian) | MR

[4] Raggi F., Rios J., Rincon H., Fernandes-Alonso R., Signoret C., “The lattice structure of preradicals”, Commun. Algebra, 1:3 (2002), 1533–1544 | DOI | MR

[5] Raggi F., Rios J., Rincon H., Fernandes-Alonso R., Signoret C., “The lattice structure of preradicals. II”, J. of Algebra and its Applications, 1:2 (2002), 201–214 | DOI | MR | Zbl

[6] Kashu A. I., “On some operations in the lattice of submodules determined by preradicals”, Bul. Acad. Ştiinţe Repub. Moldova, Matematica, 2011, no. 2(66), 5–16 | MR | Zbl

[7] 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

[8] Kashu A. I., “On inverse operations in the lattices of submodules”, Algebra and Discrete Mathematics, 13:2 (2012), 273–288 | MR | Zbl