On Jacobson – Small Submodules

  • Ali Kabban Department of mathematics, College of Science, University of Baghdad, Baghdad, Iraq
  • Wasan Khalid Department of mathematics, College of Science, University of Baghdad, Baghdad, Iraq
Keywords: J–small submodules, J–hollow modules, J–supplemented modules, weakly J–supplemented modules

Abstract

Let R be an associative ring with identity and let M be a unitary left R–module. As a generalization of small submodule , we introduce Jacobson–small submodule (briefly J–small submodule ) . We state the main properties of J–small submodules and supplying examples and remarks for this concept . Several properties of these submodules are given . Also we introduce Jacobson–hollow modules ( briefly J–hollow ) . We give a characterization of J–hollow modules and gives conditions under which the direct sum of J–hollow modules is J–hollow . We define J–supplemented modules and some types of modules that are related to J–supplemented modules and introduce properties of this types of modules . Also we discuss the relation between them with examples and remarks are needed in our work.

Published
2019-07-19
How to Cite
Kabban, A., & Khalid, W. (2019). On Jacobson – Small Submodules. Iraqi Journal of Science, 60(7), 1584-1591. https://doi.org/10.24996/ijs.2019.60.7.18
Section
Mathematics