On the Characterization of Some m-Plithogenic Vector Spaces and Their AH-Substructures Under the Condition

Ibraheem Abu Falahah¹, Abdallah Al-Husban^2,*, Mutaz M. Abbas Ali³, Ahmed A. Alsaraireh⁴, Amani Shatarah⁵, Norah Mousa Alrayes⁵

¹Department of Mathematics, Faculty of Science, The Hashemite University, P.O. Box 330127, Zarqa, 13133, Jordan

²Department of Mathematics, Faculty of Science and Technology, Irbid National University, P.O. Box: 2600 Irbid, Jordan

³Zayed Military College, Department of General Science, UAE

⁴The university of Jordan, Aqaba, Department of computer information systems

⁵Department of Mathematics, College of Science, Taibah University, Al-Madinah, Saudi Arabia

Emails: iabufalahah@hu.edu.jo; dralhosban@inu.edu.jo; Mesh451144@gmail.com; a.alsarairah@ju.edu.jo; ashatarah@taibahu.edu.sa; Nrees@taibahu.edu.sa

Abstract

This paper is concerned with studying symbolic m-plithogenic vector spaces with finite orders between 6 and 10, where it defines and characterizes the AH-subspaces, AH-kernels, and AH- linear transformations in five different symbolic m-plithogenic spaces (6-plithogenic, 7-plithogenic,10-plithogenic vector spaces). Also, we prove many theorems that describe the computation of the kernels and direct images of the plithogenic AH-linear transformations.

Keywords: 6-plithogenic vector space; 7-plithogenic AH-kernel; 8-plithogenic AH-image; 10-plithgenic space.