On Closed Quasi Principally Injective Acts over Monoids

  • Shaymaa Amer Abdul-Kareem Department of Mathematics, College of Basic Education, Mustansiriyah University, Baghdad, Iraq1
  • Ahmed Amer Abdulkareem Ministry of trade, Department of Follow-up and Monitoring Electronic
  • Yusra Amer Abdul-Kareem Ministry of trade, Department of Foreign and Economic Relations
Keywords: Quasi Principally Injective Acts, Closed Quasi Principally Injective Acts, Closed Self Principally Injective Monoid, Continuous Acts, Extending Acts, Generalization of Quasi Principally injective acts, AMS Subject Classification: 20M30, 20M99, 08B30

Abstract

The concept of closed quasi principally injective acts over monoids is introduced ,which signifies a generalization for the quasi principally injective as well as for the closed quasi injective acts. Characterization of this concept is intended to show the behavior of a closed quasi principally injective property. At the same time, some properties of closed quasi principally injective acts are examined in terms of their endomorphism monoid. Also, the characterization of a closed self-principally injective monoid is given in terms of its annihilator. The relationship between the following concepts is also studied; closed quasi principally injective acts over monoids, Hopfian, co Hopfian, and directly finite property. Ultimately, based on the results obtained, the conditions on subacts to inherit a closed quasi principally injective property were shown. Part of this paper was dedicated to studying the relationship between the classes of closed quasi principally injective acts with some generalizations of injectivity. Conclusions and future remarks of this work are given.

Published
2021-04-30
How to Cite
Abdul-Kareem, S. A., Abdulkareem, A. A., & Abdul-Kareem, Y. A. (2021). On Closed Quasi Principally Injective Acts over Monoids. Iraqi Journal of Science, 62(4), 1284-1292. https://doi.org/10.24996/ijs.2021.62.4.24
Section
Mathematics