Geodesic
$S$-second submodules of a~module
Algebra and discrete mathematics, Tome 32 (2021) no. 2, pp. 197-210.

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

Let $R$ be a commutative ring with identity and let $M$ be an $R$-module. The main purpose of this paper is to introduce and study the notion of $S$-second submodules of an $R$-module $M$ as a generalization of second submodules of $M$.
Keywords: second submodule, $S$-second submodule
Mots-clés : $S$-cotorsion-free module, simple module. 
@article{ADM_2021_32_2_a2,
     author = {F. Farshadifar},
     title = {$S$-second submodules of a~module},
     journal = {Algebra and discrete mathematics},
     pages = {197--210},
     publisher = {mathdoc},
     volume = {32},
     number = {2},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2021_32_2_a2/}
}
TY  - JOUR
AU  - F. Farshadifar
TI  - $S$-second submodules of a~module
JO  - Algebra and discrete mathematics
PY  - 2021
SP  - 197
EP  - 210
VL  - 32
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADM_2021_32_2_a2/
LA  - en
ID  - ADM_2021_32_2_a2
ER  - 
%0 Journal Article
%A F. Farshadifar
%T $S$-second submodules of a~module
%J Algebra and discrete mathematics
%D 2021
%P 197-210
%V 32
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADM_2021_32_2_a2/
%G en
%F ADM_2021_32_2_a2
F. Farshadifar. $S$-second submodules of a~module. Algebra and discrete mathematics, Tome 32 (2021) no. 2, pp. 197-210. http://geodesic.mathdoc.fr/item/ADM_2021_32_2_a2/

[1] Anderson D. D., Winders M., “Idealization of a module”, Journal of Commutative Algebra, 1:1 (2009), 3–56 | DOI | MR | Zbl

[2] Ansari-Toroghy H., Farshadifar F., “The dual notion of multiplication modules”, Taiwanese J. Math., 11:4 (2007), 1189–1201 | DOI | MR | Zbl

[3] Ansari-Toroghy H., Farshadifar F., “On the dual notion of prime submodules”, Algebra Colloq., 19, Spec 1 (2012), 1109–1116 | DOI | MR | Zbl

[4] Ansari-Toroghy H., Farshadifar F., “The dual notion of some generalizations of prime submodules”, Comm. Algebra, 39 (2011), 2396–2416 | DOI | MR | Zbl

[5] Ansari-Toroghy H., Farshadifar F., “On the dual notion of prime submodules (II)”, Mediterr. J. Math., 9:2 (2012), 329–338 | DOI | MR

[6] Ansari-Toroghy H., Farshadifar F., “Strong comultiplication modules”, CMU J. Nat. Sci., 8:1 (2009), 105–113 | MR

[7] Atiyah M. F., Macdonald I. G., Introduction to commutative algebra, Addison-Wesley, 1969 | MR | Zbl

[8] A. Barnard, “Multiplication modules”, J. Algebra, 71 (1981), 174–178 | DOI | MR | Zbl

[9] Dauns J., “Prime submodules”, J. Reine Angew. Math., 298 (1978), 156–181 | MR | Zbl

[10] Faith C., “Rings whose modules have maximal submodules”, Publ. Mat., 39 (1995), 201–214 | DOI | MR | Zbl

[11] Fuchs L., Heinzer W., Olberding B., “Commutative ideal theory without finiteness conditions: Irreducibility in the quotient filed”, Abelian Groups, Rings, Modules, and Homological Algebra, Lect. Notes Pure Appl. Math., 249, 2006, 121–145 | DOI | MR | Zbl

[12] Gilmer R., Multiplicative Ideal Theory, Queen's Papers in Pure and Applied Mathematics, 90, Queen's University, Kingston, Canada, 1992 | MR | Zbl

[13] Nagata M., Local Rings, Interscience, New York, 1962 | MR | Zbl

[14] Sevim E. S., Arabaci T., Tekir Ü., Koc S., “On S-prime submodules”, Turkish Journal of Mathematics, 43:2 (2019), 1036–1046 | DOI | MR | Zbl

[15] Wang F., Kim H., Foundations of Commutative Rings and Their Modules, Springer, Singapore, 2016 | MR | Zbl

[16] Yassemi S., “The dual notion of prime submodules”, Arch. Math. (Brno), 37 (2001), 273–278 | MR | Zbl