An Algebraic Approach to the Symbolic 5-Plithogenic Vector Spaces

Sara Sawalmeh¹, Cuauhtemoc Samaniego^2,*, Khakimova Khulkar Khamitovna³

¹Mutah University, Faculty of Science, Mutah, Jordan

²College of Business Administration, American University of the Middle East, 54200, Egaila, Kuwait

²Tashkent State University of Economics, Uzbekistan

Emails: Sarahsawalmeh98@gmail.com; jose.reyna@aum.edu.kw; x.xakimova@tsue.uz  

Abstract

The objective of this paper is to study for the first time the concept of symbolic 5-plithogenic vector space defined over symbolic 5-plithogenic field. Many results about the algebraic properties of this class of spaces will be obtained, where we define AH-subspaces, AH-linear transformations, and kernels. Also, we study the inner products defined over symbolic 5-plithogenic vector spaces and determine the conditions of orthogonality in these spaces with many interesting examples.

Keywords: symbolic 5-plithogenic vector space; AH-kernel; basis; plithogenic set