Foundations of Neutrosophic N-Semirings Theory and Structural Properties

Authors

• Raja Muhammad Hashim, Department of Mathematics and Statistics, Faculty of Natural and Computational Science, Hazara University, Mansehra, Khyber Pakhtunkhwa, PakistanFollow
• Muhammad Gulistan, Department of Mathematics and Statistics, Faculty of Natural and Computational Science, Hazara University, Mansehra, Khyber Pakhtunkhwa, PakistanFollow
• Muhammad Shahzad, Department of Mathematics and Statistics, Faculty of Natural and Computational Science, Hazara University, Mansehra, Khyber Pakhtunkhwa, PakistanFollow

Authors' ORCIDs

Raja Muhammad Hashim: https://orcid.org/0009-0003-9983-2842

Muhammad Gulistan: https://orcid.org/0000-0002-6438-1047

Muhammad Shahzad: https://orcid.org/0009-0005-3317-3455

Article Type

Research Article

Abstract

In this paper the concept of neutrosophic n-semirings (S∪ I, ∗ ₁, ∗ _2, ∗ ₃,..., ∗ _n, ∗ _n+1) has been introduced. The substructure of n-semirings (S∪ I, ∗ ₁, ∗ _2, ∗ ₃,..., ∗ _n, ∗ _n+1) has been defined and some useful results have been proved. Moreover, in order to familiarize the readers with these concepts some worthy examples have been coined. The left, right and two sided ideals of neutrosophic n-semirings have been paid a special heed. Finally we have turned our discussion towards the compatible and congruence relations and some remarkable properties have also been considered. Furthermore, we vividly have given examples to express the rationality of each notion popularized in this paper.

Keywords

Neutrosophic n-semirings, Neutrosophic sub n-semirings, Ideals and congruence, Relations in neutrosophic structures

How to Cite

Hashim, Raja Muhammad; Gulistan, Muhammad; and Shahzad, Muhammad (2026) "Foundations of Neutrosophic N-Semirings Theory and Structural Properties," Neutrosophic Systems with Applications: Vol. 26: Iss. 7, Article 2. DOI: https://doi.org/10.63689/2993-7159.1354