Relationship of Essentially Small Quasi-Dedekind Modules with Scalar and Multiplication Modules

  • Inas Salman Obaid College of Computer Science and Information Technology, Wasit University, Iraq
  • Mukdad Qaess Hussain College of Education for Pure Science, Diyala University, Diyala, Iraq
  • Darya Jabar AbdulKareem Bilad Al Rafidain University College, Diyala, Iraq
Keywords: Essentially small Quasi-Dedekind modules, scalar modules, multiplication modules

Abstract

Let be a ring with 1 and D is a left module over . In this paper, we study the relationship between essentially small quasi-Dedekind modules with scalar and multiplication modules. We show that if D is a scalar small quasi-prime -module, thus D is an essentially small quasi-Dedekind -module. We also show that if D is a faithful multiplication -module, then D is an essentially small prime -module iff is an essentially small quasi-Dedekind ring.

Published
2020-05-17
How to Cite
ObaidI. S., HussainM. Q., & AbdulKareemD. J. (2020). Relationship of Essentially Small Quasi-Dedekind Modules with Scalar and Multiplication Modules. Iraqi Journal of Science, 179-182. https://doi.org/10.24996/ijs.2020.SI.1.23