e-Subalgebras and e-Homomorphisms of PGK2-Algebras
This paper is devoted for three main purposes. First, subalgebras, e-subalgebras of a principal generalized K2-algebra (PGK2-algebra), and their associated principal generalized K2-triples are studied. We prove that every GM-subalgebra, GK-subalgebra, De Morgan subalgebra, Kleene subalgebra, and Boo...
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| Format: | Article |
| Language: | English |
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Wiley
2025-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/jom/4327085 |
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| _version_ | 1850136704306905088 |
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| author | Abd El-Mohsen Badawy Essam El-Seidy Mohiedeen Ahmed Ahmed Gaber |
| author_facet | Abd El-Mohsen Badawy Essam El-Seidy Mohiedeen Ahmed Ahmed Gaber |
| author_sort | Abd El-Mohsen Badawy |
| collection | DOAJ |
| description | This paper is devoted for three main purposes. First, subalgebras, e-subalgebras of a principal generalized K2-algebra (PGK2-algebra), and their associated principal generalized K2-triples are studied. We prove that every GM-subalgebra, GK-subalgebra, De Morgan subalgebra, Kleene subalgebra, and Boolean subalgebra of a generalized K2-algebra is a principal subalgebra. Examples are provided to determine all different types of certain principal generalized K2-algebras. Second, the completion problem concerning principal generalized K2-triples is solved and an example is given to explain how to apply it. Finally, we define homomorphisms and e-homomorphisms between two principal generalized K2-algebras. We show that every e-homomorphism determines a triple homomorphism of principal generalized K2-triples and every triple homomorphism uniquely determines an e-homomorphism of principal generalized K2-algebras. |
| format | Article |
| id | doaj-art-17a0c0ea1dfb403b999fce9b8cdfe573 |
| institution | OA Journals |
| issn | 2314-4785 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-17a0c0ea1dfb403b999fce9b8cdfe5732025-08-20T02:31:03ZengWileyJournal of Mathematics2314-47852025-01-01202510.1155/jom/4327085e-Subalgebras and e-Homomorphisms of PGK2-AlgebrasAbd El-Mohsen Badawy0Essam El-Seidy1Mohiedeen Ahmed2Ahmed Gaber3Department of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsThis paper is devoted for three main purposes. First, subalgebras, e-subalgebras of a principal generalized K2-algebra (PGK2-algebra), and their associated principal generalized K2-triples are studied. We prove that every GM-subalgebra, GK-subalgebra, De Morgan subalgebra, Kleene subalgebra, and Boolean subalgebra of a generalized K2-algebra is a principal subalgebra. Examples are provided to determine all different types of certain principal generalized K2-algebras. Second, the completion problem concerning principal generalized K2-triples is solved and an example is given to explain how to apply it. Finally, we define homomorphisms and e-homomorphisms between two principal generalized K2-algebras. We show that every e-homomorphism determines a triple homomorphism of principal generalized K2-triples and every triple homomorphism uniquely determines an e-homomorphism of principal generalized K2-algebras.http://dx.doi.org/10.1155/jom/4327085 |
| spellingShingle | Abd El-Mohsen Badawy Essam El-Seidy Mohiedeen Ahmed Ahmed Gaber e-Subalgebras and e-Homomorphisms of PGK2-Algebras Journal of Mathematics |
| title | e-Subalgebras and e-Homomorphisms of PGK2-Algebras |
| title_full | e-Subalgebras and e-Homomorphisms of PGK2-Algebras |
| title_fullStr | e-Subalgebras and e-Homomorphisms of PGK2-Algebras |
| title_full_unstemmed | e-Subalgebras and e-Homomorphisms of PGK2-Algebras |
| title_short | e-Subalgebras and e-Homomorphisms of PGK2-Algebras |
| title_sort | e subalgebras and e homomorphisms of pgk2 algebras |
| url | http://dx.doi.org/10.1155/jom/4327085 |
| work_keys_str_mv | AT abdelmohsenbadawy esubalgebrasandehomomorphismsofpgk2algebras AT essamelseidy esubalgebrasandehomomorphismsofpgk2algebras AT mohiedeenahmed esubalgebrasandehomomorphismsofpgk2algebras AT ahmedgaber esubalgebrasandehomomorphismsofpgk2algebras |