Positive implicative True-False ideals in BCK-algebras
In BCK-algebra, the concept of a positive implicative $T\&F$-ideal is introduced, and further several properties are investigated. The relationship between $T\&F$-ideals and positive implicative $T\&F$-ideals is established, and an example is given to reveal that a $T\&F$-ideal...
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| Format: | Article |
| Language: | English |
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Shahid Bahonar University of Kerman
2022-11-01
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| Series: | Journal of Mahani Mathematical Research |
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| Online Access: | https://jmmrc.uk.ac.ir/article_3324_652488ba4bd146fb12cd6ec1e9153911.pdf |
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| author | Rajabali Borzooei M. Mohseni Takallo Young Bae Jun M. Aaly Kologani |
| author_facet | Rajabali Borzooei M. Mohseni Takallo Young Bae Jun M. Aaly Kologani |
| author_sort | Rajabali Borzooei |
| collection | DOAJ |
| description | In BCK-algebra, the concept of a positive implicative $T\&F$-ideal is introduced, and further several properties are investigated. The relationship between $T\&F$-ideals and positive implicative $T\&F$-ideals is established, and an example is given to reveal that a $T\&F$-ideal is not a positive implicative $T\&F$-ideal. Various conditions under which a $T\&F$-ideal can be a positive implicative $T\&F$-ideal are explored and various characterizations of a positive implicative $T\&F$-ideal are studied. The extended property of a positive implicative $T\&F$-ideal is constructed. |
| format | Article |
| id | doaj-art-55e4bc1322a146ffb9d4abdbcd5eff9a |
| institution | Kabale University |
| issn | 2251-7952 2645-4505 |
| language | English |
| publishDate | 2022-11-01 |
| publisher | Shahid Bahonar University of Kerman |
| record_format | Article |
| series | Journal of Mahani Mathematical Research |
| spelling | doaj-art-55e4bc1322a146ffb9d4abdbcd5eff9a2025-01-07T10:26:23ZengShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-79522645-45052022-11-01113698510.22103/jmmrc.2022.19150.12163324Positive implicative True-False ideals in BCK-algebrasRajabali Borzooei0M. Mohseni Takallo1Young Bae Jun2M. Aaly Kologani3Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, IranDepartment of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, IranDepartment of Mathematics Education, Gyeongsang National University, Chinju 660-701, Republic of KoreaHatef Higher Education Institute, Zahedan, IranIn BCK-algebra, the concept of a positive implicative $T\&F$-ideal is introduced, and further several properties are investigated. The relationship between $T\&F$-ideals and positive implicative $T\&F$-ideals is established, and an example is given to reveal that a $T\&F$-ideal is not a positive implicative $T\&F$-ideal. Various conditions under which a $T\&F$-ideal can be a positive implicative $T\&F$-ideal are explored and various characterizations of a positive implicative $T\&F$-ideal are studied. The extended property of a positive implicative $T\&F$-ideal is constructed.https://jmmrc.uk.ac.ir/article_3324_652488ba4bd146fb12cd6ec1e9153911.pdftrue-false structure(limited) $t&f$-ideal(limited) positive implicative $t&f$-ideal |
| spellingShingle | Rajabali Borzooei M. Mohseni Takallo Young Bae Jun M. Aaly Kologani Positive implicative True-False ideals in BCK-algebras Journal of Mahani Mathematical Research true-false structure (limited) $t&f$-ideal (limited) positive implicative $t&f$-ideal |
| title | Positive implicative True-False ideals in BCK-algebras |
| title_full | Positive implicative True-False ideals in BCK-algebras |
| title_fullStr | Positive implicative True-False ideals in BCK-algebras |
| title_full_unstemmed | Positive implicative True-False ideals in BCK-algebras |
| title_short | Positive implicative True-False ideals in BCK-algebras |
| title_sort | positive implicative true false ideals in bck algebras |
| topic | true-false structure (limited) $t&f$-ideal (limited) positive implicative $t&f$-ideal |
| url | https://jmmrc.uk.ac.ir/article_3324_652488ba4bd146fb12cd6ec1e9153911.pdf |
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