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

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
Jul 19, 2019
How to Cite
KABBAN, Ali; KHALID, Wasan. On Jacobson – Small Submodules. Iraqi Journal of Science, [S.l.], p. 1584-1591, july 2019. ISSN 2312-1637. Available at: <http://scbaghdad.edu.iq/eijs/index.php/eijs/article/view/1002>. Date accessed: 22 aug. 2019.
Section
Mathematics