Original scientific paper

On n-absorbing submodules

Ahmad Yousefian Darani ; Department of Mathematics and Applications, University of Mohaghegh Ardabili, Ardabil, Iran
Fatemeh Soheilnia ; Department of Mathematics and Applications, University of Mohaghegh Ardabili, Ardabil, Iran

Abstract

All rings are commutative with identity, and all modules are unital. The purpose of this article is to investigate n-absorbing submodules. For this reason we introduce the concept of n-absorbing submodules generalizing n-absorbing ideals of rings. Let M be an R-module. A proper submodule N of M is called an n-absorbing submodule if whenever $a_{1}\cdots a_{n}m\in N$ for $a_{1},\ldots,a_{n}\in R$ and $m\in M$, then either $a_{1}\cdots a_{n}\in (N :_R M)$ or there are $n-1$ of $a_{i}$'s whose product with m is in N. We study the basic properties of n-absorbing submodules and then we study n-absorbing submodules of some classes of modules (e.g. Dedekind modules, Prüfer modules, etc.) over commutative rings.

Keywords

multiplication module; invertible submodule; Dedekind module; valuation module; Prüfer module; n-absorbing submodule; strongly n-absorbing submodule

Hrčak ID:

93289

URI

https://hrcak.srce.hr/93289

Publication date:

5.12.2012.

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