n-pure submodules of modules

چکیده مقاله

Let R be a commutative ring, M an R-module, and n ≥ 1 an integer. In this paper, we 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 I₁I₂…I_nN = I₁N ∩ I₂N ∩ …I_nN ∩ (I₁I₂…I_n)M for all proper ideals I₁, I₂, …I_n of R. © 2024, Qom University of Technology. All rights reserved.