On the Two-Fold Maximal Units in Some Two-Fold Finite Neutrosophic Rings Modulo Integers for

Isra Al-Shbeil^1,*, Ibraheem Abu Falahah², Talat Alkhouli³, Ahmed Soiman Rashed Alhawiti⁴, Jenan Shtayat⁵, Abdallah Al-Husban^{6, 7}

¹Department of Mathematics, faculty of science, University of Jordan, Amman 11942, Jordan

²Department of  Mathematics, Faculty of Science, The Hashemite University, P.O. Box 330127, Zarqa, 13133, Jordan

³Applied Science Department, Aqaba University College, Balqa Applied University, Jordan

⁴Department of General Studies, College Of Technology in Haql, Tabuk, Kingdom Of Saudi Arabia

⁵Department of mathematics, Yarmouk University, Irbid 21163, Jordan

⁶Department of Mathematics, Faculty of Science and Technology, Irbid National University, P.O. Box: 2600 Irbid, Jordan

⁷Jadara Research center, Jadara University, Irbid 21110, Jordan

Emails: i.shbeil@ju.edu.jo; iabufalahah@hu.edu.jo; Talat.khouli@bau.edu.jo; ahmed.a13@tvtc.gov.sa; Jenan@inu.edu.jo; dralhosban@inu.edu.jo

Abstract

 In this paper, we have defined the concept of two-fold maximal units in finite two-fold neutrosophic rings modulo integers, where a sufficient and necessary condition for such class of generalized units will be provided. We characterize all maximal units in the following two-fold neutrosophic rings   for .

Keywords: Two-fold algebra; Finite neutrosophic ring; Modulo integer ring; minimal unit