The Structure of Neutrosophic Radical of an ideal and Primary Ideal in Neutrosophic Rings

Authors

  • Murhaf Riad Alabdullah 1Faculty of Science, Department of Mathematics, University of Aleppo, Aleppo, Syria

Keywords:

Neutrosophic ring, Neutrosophic primary, Neutrosophic Radical, Ideal.

Abstract

In this study, we define radical and primary ideals as novel types of neutrosophic 
substructures within a neutrosophic ring. We investigate the properties of these substructures based 
on the characteristics of neutrosophic rings.  Finally, several examples are provided to illustrate the 
validity of the results. Although neutrosophic radical and primary ideals have intrinsic theoretical 
value, this study aims to lay the groundwork for establishing a Noether theorem on neutrosophic 
primary decompositions. 

 

DOI 10.5281/zenodo.1738751

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Published

2026-03-25

Issue

Vol. 97 (2026): Neutrosophic Sets and Systems

Section

Article

License

Copyright (c) 2025 Neutrosophic Sets and Systems

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

 Creative Commons Attribution (CC BY) license.

How to Cite

Murhaf Riad Alabdullah. (2026). The Structure of Neutrosophic Radical of an ideal and Primary Ideal in Neutrosophic Rings. Neutrosophic Sets and Systems, 97, 425-438. https://fs.unm.edu/nss8/index.php/111/article/view/7404