On Some Special Elements In Neutrosophic Rings and Refined Neutrosophic Rings

Year 2020, Issue: 33, 33 - 39, 31.12.2020

Mohammad Abobala

Abstract

Idempotent elements in a ring R are the elements with the condition a^2=a. This paper introduces the criterion of any element in a refined neutrosophic ring to be idempotent. Also, the concept of symmetric and supersymmetric elements in a neutrosophic ring R(I), and a refined neutrosophic ring R(I_1,I_2) are defined. Also, the invertibility of these elements is discussed.

Keywords

refined neutrosophic ring, Neutrosophic ring, idempotent element, symmetric element, supersymmetric element

References

• M. Abobala, On Some Special Substructures of Neutrosophic Rings and Their Properties, International Journal of Neutrosophic Science 4 (2020) 72-81.
• M. Abobala, Classical Homomorphisms Between Refined Neutrosophic Rings and Neutrosophic Rings, International Journal of Neutrosophic Science 5 (2020) 72-75.
• M. Abobala, AH-Subspaces in Neutrosophic Vector Spaces, International Journal of Neutrosophic Science 6 (2020) 80-86.
• M. Abobala, R. Alhamido, AH-Substructures in Neutrosophic Modules, International Journal of Neutrosophic Science 7 (2020) 79-86.
• M. Abobala, Classical Homomorphisms Between n-refined Neutrosophic Rings, International Journal of Neutrosophic Science 7 (2020) 74-78.
• A. Hatip, N. Olgun, On Refined Neutrosophic R-Module, International Journal of Neutrosophic Science 7 (2020) 87-96.
• M. Abobala, On Some Special Substructures of Refined Neutrosophic Rings, International Journal of Neutrosophic Science 5 (2020) 59-66.
• A. A. A. Agboola, On Refined Neutrosophic Algebraic Structures, Neutrosophic Sets and Systems 10 (2015) 99-101.
• E. O. Adeleke, A. A. A. Agboola, F. Smarandache, Refined Neutrosophic Rings I, International Journal of Neutrosophic Science 2(2) (2020) 77-81.
• E. O. Adeleke, A. A. A. Agboola, F. Smarandache, Refined Neutrosophic Rings II, International Journal of Neutrosophic Science 2(2) (2020) 89-94.
• V. W. B. Kandasamy, F. Smarandache, Some Neutrosophic Algebraic Structures and Neutrosophic N-Algebraic Structures, Hexis, Phoenix, Arizona, 2006.
• F. Smarandache, M. Abobala, n-Refined Neutrosophic Rings, International Journal of Neutrosophic Science 6 (2020) 83-90.
• F. Smarandache, M. Abobala, n-Refined Neutrosophic Vector Spaces, International Journal of Neutrosophic Science 7 (2020) 47-54.
• T. Chalapathi, L. Madhavi, Neutrosophic Boolean Rings, Neutrosophic Sets and Systems 33 (2020) 57-66.
• Y. Ma, X. Zhang, F. Smarandache, J. Zhang. The Structure of Idempotents in Neutrosophic Rings and Neutrosophic Quadruple Rings, Symmetry 11(10) (2019) 1-15.
• V. W. B. Kandasamy, K. Ilanthenral, F. Smarandache, Semi-idempotents in Neutrosophic Rings, Mathematics 7 (2019) 1-7.
• M. A. Ibrahim, A. A. A. Agboola, B. S. Badmus, S. A. Akinleye, On Refined Neutrosophic Vector Spaces I, International Journal of Neutrosophic Science 7 (2020) 97-109.