Mathematics and Computational Sciences

$n$-pure submodules of modules

Document Type : Original Article

Author

Faranak Farshadifar

Department of Mathematics Education, Farhangian University, P.O. Box 14665-889, Tehran, Iran

https://doi.org/10.30511/mcs.2024.2035103.1203
Abstract
‎Let $R$ be a commutative ring‎, ‎$M$ an $R$-module‎, ‎and $n\geq 1$ 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 \emph {$n$-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 $R$‎.

Keywords

Pure submodules‎
‎$n$-pure submodule‎
‎Multiplication module‎
‎Fully $n$-pure module

Subjects

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Mathematics and Computational Sciences
Volume 5, Issue 4
Autumn 2024
Pages 48-53

  • Receive Date 09 July 2024
  • Revise Date 01 November 2024
  • Accept Date 07 November 2024

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