ON NIL-SYMMETRIC RINGS AND MODULES SKEWED BY RING ENDOMORPHISM

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 an...

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Bibliographic Details
Published in:Science journal of University of Zakho (Online) Vol. 13; no. 3; pp. 348 - 356
Main Authors: Mustafa, Ibrahim, Ahmed, Chnar Abdulkareem
Format: Journal Article
Language:English
Published: University of Zakho 03.07.2025
Subjects:
Flat Module
Polynomial Module
Reduced-Ring
Symmetric Ring
Ճ-Reduced Module
ISSN:2663-628X, 2663-6298
Online Access:Get full text
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Summary: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
ISSN:2663-628X
2663-6298
DOI:10.25271/sjuoz.2025.13.3.1492