ON NIL-SYMMETRIC RINGS AND MODULES SKEWED BY RING ENDOMORPHISM

Authors

  • Ibrahim Adnan Mustafa Department of Mathematics, College of Science, University of Zakho, Zakho, Kurdistan Region, Iraq
  • Chenar Abdulkareem Ahmed Department of Mathematics, College of Science, University of Zakho, Zakho, Kurdistan Region, Iraq

DOI:

https://doi.org/10.25271/sjuoz.2025.13.3.1492

Keywords:

Reduced-Ring, Symmetric Ring, Flat Module, Ճ-Reduced Module, Polynomial Module

Abstract

The symmetric property plays an important role in non-commutative ring theory and module theory.  In this paper, we study the symmetric property with one element of the ring  and two nilpotent elements of  skewed by ring endomorphism  on rings, introducing the concept of a right - -symmetric ring and extend the concept of right - -symmetric rings to modules by introducing another concept called the right - -symmetric module which is a generalization of -symmetric modules. According to this, we examine the characterization of a right - -symmetric ring and a right  - -symmetric module and their related properties including ring and explore their connections to other classes of rings and modules.   Furthermore, we investigate the concept of - -symmetric on some ring extensions and localizations like  Dorroh extension, Jordan extension and module localizations like

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Published

2025-07-03

How to Cite

Mustafa, I., & Ahmed, C. A. (2025). ON NIL-SYMMETRIC RINGS AND MODULES SKEWED BY RING ENDOMORPHISM. Science Journal of University of Zakho, 13(3), 348–356. https://doi.org/10.25271/sjuoz.2025.13.3.1492

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Section

Science Journal of University of Zakho