$n$-pure submodules of modules - Faranak Farshadifar (Mathematics and Computational Sciences)
‎Let $R$ be a commutative ring‎, ‎$M$ an $R$-module‎, ‎and $n≥ 1$ an integer‎. ‎In this paper‎, ‎we will introduce the concept of $n$-pure submodules of $M$ as a generalization of pure submodules and obtain some related results‎.‎We say that a submodule $N$ of $M$ is a $n$-pure submodule of $M$ if $I_1I_2...I_nN=I_1N \cap I_2N\cap...I_nN\cap (I_1I_2...I_n)M$ for all proper ideals $I_1‎, ‎I_2,...I_n$ of $R$‎.