Symbolic 4-Plithogenic Rings and 5-Plithogenic Rings
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 ring...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-08-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/8/1588 |
| _version_ | 1797583135994544128 |
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| author | Ahmed Hatip |
| author_facet | Ahmed Hatip |
| author_sort | Ahmed Hatip |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T23:32:31Z |
| format | Article |
| id | doaj.art-526ffd798f904d1aa2d31d814890d47a |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T23:32:31Z |
| publishDate | 2023-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-526ffd798f904d1aa2d31d814890d47a2023-11-19T03:11:55ZengMDPI AGSymmetry2073-89942023-08-01158158810.3390/sym15081588Symbolic 4-Plithogenic Rings and 5-Plithogenic RingsAhmed Hatip0Department of Mathematics, Gaziantep University, Gaziantep 27310, TurkeySymbolic 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.https://www.mdpi.com/2073-8994/15/8/1588symbolic 4-plithogenic ring4-plithogenic ah-ideal4-plithogenic ah-homomorphismsymbolic 5-plithogenic ring5-plithogenic ah-ideal5-plithogenic ah-homomorphism |
| spellingShingle | Ahmed Hatip Symbolic 4-Plithogenic Rings and 5-Plithogenic Rings Symmetry symbolic 4-plithogenic ring 4-plithogenic ah-ideal 4-plithogenic ah-homomorphism symbolic 5-plithogenic ring 5-plithogenic ah-ideal 5-plithogenic ah-homomorphism |
| title | Symbolic 4-Plithogenic Rings and 5-Plithogenic Rings |
| title_full | Symbolic 4-Plithogenic Rings and 5-Plithogenic Rings |
| title_fullStr | Symbolic 4-Plithogenic Rings and 5-Plithogenic Rings |
| title_full_unstemmed | Symbolic 4-Plithogenic Rings and 5-Plithogenic Rings |
| title_short | Symbolic 4-Plithogenic Rings and 5-Plithogenic Rings |
| title_sort | symbolic 4 plithogenic rings and 5 plithogenic rings |
| topic | symbolic 4-plithogenic ring 4-plithogenic ah-ideal 4-plithogenic ah-homomorphism symbolic 5-plithogenic ring 5-plithogenic ah-ideal 5-plithogenic ah-homomorphism |
| url | https://www.mdpi.com/2073-8994/15/8/1588 |
| work_keys_str_mv | AT ahmedhatip symbolic4plithogenicringsand5plithogenicrings |