Geodesic
Generalized $2$-absorbing and strongly generalized $2$-absorbing second submodules
Algebra and discrete mathematics, Tome 29 (2020) no. 2, pp. 161-172

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Let $R$ be a commutative ring with identity. A proper submodule $N$ of an $R$-module $M$ is said to be a $2$-absorbing submodule of $M$ if whenever $abm \in N$ for some $a, b \in R$ and $m \in M$, then $am \in N$ or $bm \in N$ or $ab \in (N :_R M)$. In [3], the authors introduced two dual notion of $2$-absorbing submodules (that is, $2$-absorbing and strongly $2$-absorbing second submodules) of $M$ and investigated some properties of these classes of modules. In this paper, we will introduce the concepts of generalized $2$-absorbing and strongly generalized $2$-absorbing second submodules of modules over a commutative ring and obtain some related results.
Keywords: second, generalized $2$-absorbing second. 
@article{ADM_2020_29_2_a2,
     author = {H. Ansari-Toroghy and F. Farshadifar and S. Maleki-Roudposhti},
     title = {Generalized $2$-absorbing and strongly generalized $2$-absorbing second submodules},
     journal = {Algebra and discrete mathematics},
     pages = {161--172},
     publisher = {mathdoc},
     volume = {29},
     number = {2},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2020_29_2_a2/}
}
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H. Ansari-Toroghy; F. Farshadifar; S. Maleki-Roudposhti. Generalized $2$-absorbing and strongly generalized $2$-absorbing second submodules. Algebra and discrete mathematics, Tome 29 (2020) no. 2, pp. 161-172. http://geodesic.mathdoc.fr/item/ADM_2020_29_2_a2/