A new kind of soft algebraic structures: bipolar soft Lie algebras
In this paper, basic concepts of soft set theory was mentioned. Then, bipolar soft Lie algebras and bipolar soft Lie ideals were defined with the help of soft sets. Some algebraic properties of the new concepts were investigated. The relationship between the two structures were analyzed. Also, it wa...
| Main Author: | |
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| Format: | Article |
| Language: | English |
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Vasyl Stefanyk Precarpathian National University
2022-12-01
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| Series: | Karpatsʹkì Matematičnì Publìkacìï |
| Subjects: | |
| Online Access: | https://journals.pnu.edu.ua/index.php/cmp/article/view/4886 |
| _version_ | 1797205792124829696 |
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| author | F. Çıtak |
| author_facet | F. Çıtak |
| author_sort | F. Çıtak |
| collection | DOAJ |
| description | In this paper, basic concepts of soft set theory was mentioned. Then, bipolar soft Lie algebras and bipolar soft Lie ideals were defined with the help of soft sets. Some algebraic properties of the new concepts were investigated. The relationship between the two structures were analyzed. Also, it was proved that the level cuts of a bipolar soft Lie algebra were Lie subalgebras of a Lie algebra by the new definitions. After then, soft image and soft preimage of a bipolar soft Lie algebra/ideal were proved to be a bipolar soft Lie algebra/ideal. |
| first_indexed | 2024-04-24T08:56:45Z |
| format | Article |
| id | doaj.art-75e17c1b32cf4f8b9f81e53efa811d3f |
| institution | Directory Open Access Journal |
| issn | 2075-9827 2313-0210 |
| language | English |
| last_indexed | 2024-04-24T08:56:45Z |
| publishDate | 2022-12-01 |
| publisher | Vasyl Stefanyk Precarpathian National University |
| record_format | Article |
| series | Karpatsʹkì Matematičnì Publìkacìï |
| spelling | doaj.art-75e17c1b32cf4f8b9f81e53efa811d3f2024-04-16T07:12:26ZengVasyl Stefanyk Precarpathian National UniversityKarpatsʹkì Matematičnì Publìkacìï2075-98272313-02102022-12-0114246447410.15330/cmp.14.2.464-4744253A new kind of soft algebraic structures: bipolar soft Lie algebrasF. Çıtak0https://orcid.org/0000-0003-1784-1845Tokat Gaziosmanpaşa University, Taşlıçiftlik Campus, 60250 Tokat, TürkiyeIn this paper, basic concepts of soft set theory was mentioned. Then, bipolar soft Lie algebras and bipolar soft Lie ideals were defined with the help of soft sets. Some algebraic properties of the new concepts were investigated. The relationship between the two structures were analyzed. Also, it was proved that the level cuts of a bipolar soft Lie algebra were Lie subalgebras of a Lie algebra by the new definitions. After then, soft image and soft preimage of a bipolar soft Lie algebra/ideal were proved to be a bipolar soft Lie algebra/ideal.https://journals.pnu.edu.ua/index.php/cmp/article/view/4886soft setsoft lie algebrasoft lie idealbipolar soft lie algebrabipolar soft lie ideal |
| spellingShingle | F. Çıtak A new kind of soft algebraic structures: bipolar soft Lie algebras Karpatsʹkì Matematičnì Publìkacìï soft set soft lie algebra soft lie ideal bipolar soft lie algebra bipolar soft lie ideal |
| title | A new kind of soft algebraic structures: bipolar soft Lie algebras |
| title_full | A new kind of soft algebraic structures: bipolar soft Lie algebras |
| title_fullStr | A new kind of soft algebraic structures: bipolar soft Lie algebras |
| title_full_unstemmed | A new kind of soft algebraic structures: bipolar soft Lie algebras |
| title_short | A new kind of soft algebraic structures: bipolar soft Lie algebras |
| title_sort | new kind of soft algebraic structures bipolar soft lie algebras |
| topic | soft set soft lie algebra soft lie ideal bipolar soft lie algebra bipolar soft lie ideal |
| url | https://journals.pnu.edu.ua/index.php/cmp/article/view/4886 |
| work_keys_str_mv | AT fcıtak anewkindofsoftalgebraicstructuresbipolarsoftliealgebras AT fcıtak newkindofsoftalgebraicstructuresbipolarsoftliealgebras |