Document Type : Research Paper

Author

Department of Mathematics, Faculty of Science, Tishreen University, Lattakia, Syria.

Abstract

If R is a ring, then Rn(I) is called a refined neutrosophic ring. Every AH-subset of Rn(I) has the form P = ∑ni=0 p i Ii= {a0+a1I+⋯+anIn: ai∈p i}, where p i are subsets of the classical ring R. The objective of this paper is to determine the necessary and sufficient conditions on p i which make P be an ideal of Rn(I). Also, this work introduces a full description of the algebraic structure and form for AH-maximal and minimal ideals in Rn(I).

Keywords

Main Subjects

  1. Smarandache, F., & Abobala, M. (2020). n-Refined neutrosophic rings. International journal of neutrosophic science, 5, 83-90.
  2. Sankari, H., & Abobala, M. (2020). n-refined neutrosophic modules. Neutrosophic sets and systems, 36, 1-11.
  3. Sankari, H., & Abobala, M. (2020). AH-Homomorphisms in neutrosophic rings and refined neutrosophic rings. Neutrosophic sets and systems, 38.
  4. Kandasamy, W. V., & Smarandache, F. (2006). Some neutrosophic algebraic structures and neutrosophic n-algebraic structures. Infinite Study.
  5. Smarandache F., and Abobala, M. (2020). n-refined neutrosophic vector spaces. International journal of neutrosophic science, 7(1), 47-54.
  6. Abobala, M., Hatip, A., & Alhamido, R. (2019). A contribution to neutrosophic groups. International journal of neutrosophic science, 0(2), 67-76.
  7. Abdel-Basset, M., Gamal, A., Son, L. H., & Smarandache, F. (2020). A bipolar neutrosophic multi criteria decision making framework for professional selection. Applied sciences10(4), 1202. https://doi.org/10.3390/app10041202
  8. Abdel-Basset, M., Mohamed, R., Zaied, A. E. N. H., Gamal, A., & Smarandache, F. (2020). Solving the supply chain problem using the best-worst method based on a novel Plithogenic model. In Optimization theory based on neutrosophic and plithogenic sets(pp. 1-19). Academic Press.
  9. Abobala, M. (2019). n-refined neutrosophic groups I. International journal of neutrosophic science, 0(1), 27-34.
  10. Agboola, A. A. A., Akwu, A. D., & Oyebo, Y. T. (2012). Neutrosophic groups and subgroups. International .J .Math. Combin, 3, 1-9. http://mathcombin.com/upload/file/20150127/1422320633982016018.pdf#page=6 http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.641.3352&rep=rep1&type=pdf
  11. Abdel-Basset, M., Manogaran, G., Gamal, A., & Chang, V. (2019). A novel intelligent medical decision support model based on soft computing and IoT. IEEE internet of things journal7(5), 4160-4170.
  12. Smarandache, F. (2013). n-Valued refined neutrosophic logic and its applications to physics. Progress in physics, 4, 143-146.
  13. Abobala, M., & Lattakia, S. (2020). Classical homomorphisms between n-refined neutrosophic rings. International journal of neutrosophic science7, 74-78.
  14. Alhabib, R., & Salama, A. A. (2020). the neutrosophic time series-study its models (linear-logarithmic) and test the coefficients significance of its linear model. Neutrosophic sets and systems33, 105-115.
  15. Abdel-Basset, M., Mohamed, M., Elhoseny, M., Chiclana, F., & Zaied, A. E. N. H. (2019). Cosine similarity measures of bipolar neutrosophic set for diagnosis of bipolar disorder diseases. Artificial intelligence in medicine101, 101735. https://doi.org/10.1016/j.artmed.2019.101735
  16. Sankari, H., & Abobala, M. (2020). Neutrosophic linear diophantine equations with two variables(Vol. 38). Infinite Study.
  17. Abobala, M. (2020). Ah-subspaces in neutrosophic vector spaces. International journal of neutrosophic science6, 80-86.
  18. Edalatpanah, S. A. (2020). Systems of neutrosophic linear equations. Neutrosophic sets and systems33(1), 92-104.
  19. Abobala, M. (2020). A study of ah-substructures in n-refined neutrosophic vector spaces. International journal of neutrosophic science9, 74-85.
  1. Abobala, M. (2021). Foundations of neutrosophic number theory. Neutrosophic sets and systems39(1), 10.
  2. Abobala, M. (2020). On some neutrosophic algebraic equations. Journal of new theory, (33), 26-32.
  3. Abobala, M. (2021). Semi homomorphisms and algebraic relations between strong refined neutrosophic modules and strong neutrosophic modules. Neutrosophic sets and systems39(1), 9. https://digitalrepository.unm.edu/cgi/viewcontent.cgi?article=1748&context=nss_journal