Symbolic 4-Plithogenic Rings and 5-Plithogenic Rings

Abstract

Symbolic n-plithogenic algebraic structures are considered as symmetric generalizations of classical algebraic structures because they have n + 1 symmetric components. This paper is dedicated to generalizing symbolic 3-plithogenic rings by defining symbolic 4-plithogenic rings and 5-plithogenic rings; these new classes of n-symbolic plithogenic algebraic structures will be defined for the first time, and their algebraic substructures will be studied. AH structures are considered to be a sign of the presence of symmetry within these types of ring, as they consist of several parts that are similar in structure and symmetrical, and when combined with each other, they have a broader structure resembling the classical consonant structure. Many related substructures will be presented such as 4-plithogenic/5-plithogenic AH-ideals, 4-plithogenic/5-plithogenic AH-homomorphisms, and 4-plithogenic AHS-isomorphisms will be discussed. We will show our results in terms of theorems, with many clear numerical examples that explain the novelty of this work.