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The Structure of Regular in Symbolic 2-Plithogenic Rings and the Most Important Properties of Their Elements

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  • Murhaf Riad Alabdullah

Abstract

In this paper, we generalize the regularity to a symbolic 2-plithogenic structure. We present the structure and elementary properties of regular symbolic 2-plithogenic rings. We also found that the classical regular ring R is equivalent to the symbolic 2-plithogenic ring 2−SPR. In addition, we obtained several important results. The most important of these are as follows: U2−SPR⊆Reg2−SPR. U2−SPR∩Z2−SPR=∅. U2−SPR∩Id2−SPR=1. Id2−SPR∩N2−SPR=0. 2−SPR is regular iff R is regular. We presented a rule for finding the element that satisfies the regularity condition for any element of the regular symbolic 2-plithogenic field. The center of the regular symbolic 2-plithogenic ring is also a regular.

Suggested Citation

  • Murhaf Riad Alabdullah, 2025. "The Structure of Regular in Symbolic 2-Plithogenic Rings and the Most Important Properties of Their Elements," Journal of Mathematics, Hindawi, vol. 2025, pages 1-14, November.
    • Handle: RePEc:hin:jjmath:3291008
    DOI: 10.1155/jom/3291008
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