Year: 2020
Type: preprint
Abstract: In this study, we aim to introduce the concept of a 1-absorbing prime submodule of an unital module over a commutative ring with a non-zero identity. Let M be an R-module and N be a proper submodule of M. For all non-unit elements a, b in R and m in M if abm in N, either ab in (N : M) or m in N, then N is called 1-absorbing prime submodule of M. We show that the new concept is a generalization of prime submodules at the same time it is a kind of special 2-absorbing submodule. In addition to some properties of a 1-absorbing prime submodule, we obtain a characterization of it in a multiplication module.
Source: arXiv (Cornell University)
Author: Ugurlu, Emel Aslankarayigit
Institution: Marmara University
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3038581001