For some results of semisecond submodules

• Published in: Ibn Al-Haitham Journal for Pure and Applied Sciences Vol. 31; no. 3; pp. 102 - 108
• Main Author: Khalaf, Rasha Ibrahim
• Format: Journal Article
• Language: English
• Published: Baghdad, Iraq University of Baghdad, College of Education for Pure Science / Ibn al-Haitham 13-11-2018; University of Baghdad
• Subjects: Semisecond submodules, second submodules, secondary submodules
• ISSN: 1609-4042; 2521-3407
• DOI: 10.30526/31.3.1999

  Let â„› be a commutative ring with unity and let ℬ be a unitary R-module. Let ℵ be a proper submodule of ℬ, ℵ is called semisecond submodule if for any r∈ℛ, r≠0, n∈Z+, either rnℵ=0 or rnℵ=rℵ.
In this work, we introduce the concept of semisecond submodule and confer numerous properties concerning with this notion. Also we study semisecond modules as a popularization of second modules, where an ℛ-module ℬ is called semisecond, if ℬ is semisecond submodul of ℬ.