Small  Quasi Primary  Submodules

Authors

  • Adwia J. Abdul-Alkalik Directorate General of Education in Diyala, Ministry of Education, Diyala, Iraq.

Keywords:

Quasi Primary Submodules, Small Primary Submodules, Small Quasi Primary Submodules

Abstract

In this research, a new concept (small quasi-primary submodules) has been presented, which is a generalization of a previously studied concept (quasi-primary submodules) and a comprehensive study of it in terms of features and properties. We have also given some examples and observations about it. Its relationship with previously studied concepts was studied, and the equivalence, under certain conditions, between these concepts and the new concept was demonstrated.

References

[1] Smith, P. F.; "Primary module over commutative rings". Glasgow J . Math. , 43(1): 103-111, 2001.

[2] Adwia , J. A. ; "Primary Modules ". M. Sc, Thesis, College of Education for Pure Science Ibn -Al- Haitham , University of Baghdad, Baghdad, 2005.

[3] Adwia , J. A. ; "On Small Primary Modules". Iraqi J. Sci., 62(4): 1307-1313, 2021.

[4] Inoue, T. ; " Sum of Hollow Modules". Osaka J . Math. 20 (2), 331- 336,1983.

[5] Nuhad , S. ; Husain, A. ; " On Quasi- Small Prime Sumodules". Iraqi J. Sci., 63(4): 1692-1699, 2022.

[6] Patrick, F. ;" Hollow Modules and Local Endomorphism Rings". Pac J Math. , 53 (2): 379-385 , 1974.

[7] Layal, S. M. ; "Small Prime Modules and Small Prime Submodules". Al-Nahrain J. . Sci. , 15(4): 191-199, 2012.

[8] Iman, A. , I. ; "Some Generalization of Projective Modules". Ph. D,. Thesis, College of Science, University of Baghdad, Baghdad, 2004.

[9] Smith, P. F.; "Some Remarks on Multiplication Modules ". Arch J. Math. , 50 (3): 223-235, 1988.

Downloads

Published

2025-09-15

Issue

Section

Mathematics

How to Cite

(1)
J. Abdul-Alkalik, A. . Small  Quasi Primary  Submodules. Al-Nahrain J. Sci. 2025, 28 (3), 125-129.