Strong GE-Filters and GE-Ideals of Bordered GE-Algebras
The notion of strong GE-filters and GE-ideals (generated) is introduced, and the related properties are investigated. The intersection of strong GE-filters (resp., GE-ideals) is proved to be a strong GE-filter (resp., GE-ideal), and the union of strong GE-filters (resp., GE-ideals) is generally not...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/5520023 |
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| author | Mehmet Ali Öztürk Jeong-Gon Lee Ravikumar Bandaru Young Bae Jun |
| author_facet | Mehmet Ali Öztürk Jeong-Gon Lee Ravikumar Bandaru Young Bae Jun |
| author_sort | Mehmet Ali Öztürk |
| collection | DOAJ |
| description | The notion of strong GE-filters and GE-ideals (generated) is introduced, and the related properties are investigated. The intersection of strong GE-filters (resp., GE-ideals) is proved to be a strong GE-filter (resp., GE-ideal), and the union of strong GE-filters (resp., GE-ideals) is generally not a strong GE-filters (resp., GE-ideal) by example. Conditions for a subset of a bordered GE-algebra to be a strong GE-filter are provided, and a characterization of a strong GE-filter is considered. In order to do so, irreducible GE-filter is defined first and its properties are examined. Conditions for a GE-filter to be irreducible are discussed. Given a GE-filter, and a subset in a bordered GE-algebra, the existence of an irreducible GE-filter, which contains the given GE-filter and is disjoint to the given subset, is considered. Conditions under which any subset of a bordered GE-algebra can be a GE-ideal are provided, and GE-ideal that is generated from a subset in a bordered GE-algebra is discussed. Also, what element it is formed into is stated. Finally, the smallest GE-ideal which contains a given GE-ideal and an element in a bordered GE-algebra is established. |
| format | Article |
| id | doaj-art-bf92d558b0194e1fb76a862c8cc8bb0b |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-bf92d558b0194e1fb76a862c8cc8bb0b2025-02-03T01:28:26ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/55200235520023Strong GE-Filters and GE-Ideals of Bordered GE-AlgebrasMehmet Ali Öztürk0Jeong-Gon Lee1Ravikumar Bandaru2Young Bae Jun3Department of Mathematics, Faculty of Arts and Sciences, Adıyaman University, 02040 Adıyaman, TurkeyDivision of Applied Mathematics, Wonkwang University, Iksan-daero, Iksan-Si, Jeonbuk 54538, Republic of KoreaDepartment of Mathematics, GITAM (Deemed to be University), Hyderabad, Telangana-502329, IndiaDepartment of Mathematics Education, Gyeongsang National University, Jinju 52828, Republic of KoreaThe notion of strong GE-filters and GE-ideals (generated) is introduced, and the related properties are investigated. The intersection of strong GE-filters (resp., GE-ideals) is proved to be a strong GE-filter (resp., GE-ideal), and the union of strong GE-filters (resp., GE-ideals) is generally not a strong GE-filters (resp., GE-ideal) by example. Conditions for a subset of a bordered GE-algebra to be a strong GE-filter are provided, and a characterization of a strong GE-filter is considered. In order to do so, irreducible GE-filter is defined first and its properties are examined. Conditions for a GE-filter to be irreducible are discussed. Given a GE-filter, and a subset in a bordered GE-algebra, the existence of an irreducible GE-filter, which contains the given GE-filter and is disjoint to the given subset, is considered. Conditions under which any subset of a bordered GE-algebra can be a GE-ideal are provided, and GE-ideal that is generated from a subset in a bordered GE-algebra is discussed. Also, what element it is formed into is stated. Finally, the smallest GE-ideal which contains a given GE-ideal and an element in a bordered GE-algebra is established.http://dx.doi.org/10.1155/2021/5520023 |
| spellingShingle | Mehmet Ali Öztürk Jeong-Gon Lee Ravikumar Bandaru Young Bae Jun Strong GE-Filters and GE-Ideals of Bordered GE-Algebras Journal of Mathematics |
| title | Strong GE-Filters and GE-Ideals of Bordered GE-Algebras |
| title_full | Strong GE-Filters and GE-Ideals of Bordered GE-Algebras |
| title_fullStr | Strong GE-Filters and GE-Ideals of Bordered GE-Algebras |
| title_full_unstemmed | Strong GE-Filters and GE-Ideals of Bordered GE-Algebras |
| title_short | Strong GE-Filters and GE-Ideals of Bordered GE-Algebras |
| title_sort | strong ge filters and ge ideals of bordered ge algebras |
| url | http://dx.doi.org/10.1155/2021/5520023 |
| work_keys_str_mv | AT mehmetaliozturk stronggefiltersandgeidealsofborderedgealgebras AT jeonggonlee stronggefiltersandgeidealsofborderedgealgebras AT ravikumarbandaru stronggefiltersandgeidealsofborderedgealgebras AT youngbaejun stronggefiltersandgeidealsofborderedgealgebras |