Hom-structures and bihom-structures of antiflexible and pre-antiflexible algebras
UDC 512.554, 512.628 We define and study the structures of Pre-Anti-Flexible algebras in the Hom- and BiHom-cases. More precisely, in the BiHom-case, the corresponding algebraic structure is defined by two products $\triangleleft,$ $\triangleright$ and two linear maps $f$ and $g$ on $A.$ This struct...
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| Datum: | 2026 |
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| Sprache: | Englisch |
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Institute of Mathematics, NAS of Ukraine
2026
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/9598 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1871646584056315904 |
|---|---|
| author | Aloulou, Walid Jebli, Mansour Aloulou, Walid Jebli, Mansour |
| author_facet | Aloulou, Walid Jebli, Mansour Aloulou, Walid Jebli, Mansour |
| author_institution_txt_mv | [
{
"author": "Walid Aloulou",
"institution": "University of Sousse, ESSTHS Laboratory of Mathematical Physics, Special Fonctions and Applications (MAPSFA), Hamman-Sousse, Tunisia"
},
{
"author": "Mansour Jebli",
"institution": "University of Sfax, Faculty of Sciences, Sfax, Tunisia"
}
] |
| author_sort | Aloulou, Walid |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-07-24T15:24:12Z |
| description | UDC 512.554, 512.628
We define and study the structures of Pre-Anti-Flexible algebras in the Hom- and BiHom-cases. More precisely, in the BiHom-case, the corresponding algebraic structure is defined by two products $\triangleleft,$ $\triangleright$ and two linear maps $f$ and $g$ on $A.$ This structure is denoted by $\big(A,\triangleleft,\triangleright,f,g\big)$ and if $f=g,$ then we get the Hom-version denoted by $\big(A,\triangleleft,\triangleright,f\big).$ Our main results can be desribed as follows: we define some algebraic structures and investigate some properties and relationships between the BiHom-Pre-Anti-Flexible algebras and BiHom-Anti-Flexible algebras. Furthermore, we prove that any BiHom-Anti-Flexible algebra equipped with a Rota–Baxter operator defines a BiHom-Pre-Anti-Flexible algebra. Finally, we introduce the notion of Nijenhuis operator in the BiHom setting and demonstrate that a Nijenhuis operator on a BiHom-Anti-Flexible algebra specifies a BiHom-Pre-Anti-Flexible algebra. |
| doi_str_mv | 10.3842/umzh.v78i7-8.9598 |
| first_indexed | 2026-07-25T01:01:16Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-9598 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-07-25T01:01:16Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-95982026-07-24T15:24:12Z Hom-structures and bihom-structures of antiflexible and pre-antiflexible algebras Hom-structures and bihom-structures of antiflexible and pre-antiflexible algebras Aloulou, Walid Jebli, Mansour Aloulou, Walid Jebli, Mansour anti-flexible algebras pre-anti-flexible algebras Rota-Baxter operators Nijenhuis operators anti-flexible algebras, pre-anti-flexible algebras, Rota-Baxter operators, Nijenhuis operators UDC 512.554, 512.628 We define and study the structures of Pre-Anti-Flexible algebras in the Hom- and BiHom-cases. More precisely, in the BiHom-case, the corresponding algebraic structure is defined by two products $\triangleleft,$ $\triangleright$ and two linear maps $f$ and $g$ on $A.$ This structure is denoted by $\big(A,\triangleleft,\triangleright,f,g\big)$ and if $f=g,$ then we get the Hom-version denoted by $\big(A,\triangleleft,\triangleright,f\big).$ Our main results can be desribed as follows: we define some algebraic structures and investigate some properties and relationships between the BiHom-Pre-Anti-Flexible algebras and BiHom-Anti-Flexible algebras. Furthermore, we prove that any BiHom-Anti-Flexible algebra equipped with a Rota–Baxter operator defines a BiHom-Pre-Anti-Flexible algebra. Finally, we introduce the notion of Nijenhuis operator in the BiHom setting and demonstrate that a Nijenhuis operator on a BiHom-Anti-Flexible algebra specifies a BiHom-Pre-Anti-Flexible algebra. УДК 512.554, 512.628 Hom- та bihom-структури антигнучких і пре-антигнучких алгебр Визначено та досліджено структури пре-антигнучких алгебр у випадках Hom- і BiHom-алгебр. Зокрема, у випадку BiHom-алгебри цю алгебраїчну структуру задано двома добутками $\triangleleft,$ $\triangleright$ і двома лінійними відображеннями $f$ і $g$ на $A$ та позначено таким чином: $\big(A,\triangleleft,\triangleright,f,g\big).$ Якщо $f=g,$ то ми одержуємо Hom-версію, яку позначено так: $\big(A,\triangleleft,\triangleright,f\big).$ Основні результати статті присвячено визначенню деяких алгебраїчних структур, а також дослідженню властивостей і взаємозв'язків між BiHom-пре-антигнучкими та BiHom-антигнучкими алгебрами. Крім того, доведено, що кожна BiHom-антигнучка алгебра, наділена оператором Рота–Бакстера, породжує структуру BiHom-пре-антигнучкої алгебри. Насамкінець введено поняття оператора Нейєнхейса в BiHom-випадку та показано, що оператор Нейєнхейса на BiHom-антигнучкій алгебрі породжує BiHom-пре-антигнучку алгебру. Institute of Mathematics, NAS of Ukraine 2026-07-24 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/9598 10.3842/umzh.v78i7-8.9598 Ukrains’kyi Matematychnyi Zhurnal; Vol. 78 No. 7-8 (2026); 588–589 Український математичний журнал; Том 78 № 7-8 (2026); 588–589 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/9598/10677 Copyright (c) 2026 Walid Aloulou, Mansour Jebli |
| spellingShingle | Aloulou, Walid Jebli, Mansour Aloulou, Walid Jebli, Mansour Hom-structures and bihom-structures of antiflexible and pre-antiflexible algebras |
| title | Hom-structures and bihom-structures of antiflexible and pre-antiflexible algebras |
| title_alt | Hom-structures and bihom-structures of antiflexible and pre-antiflexible algebras |
| title_full | Hom-structures and bihom-structures of antiflexible and pre-antiflexible algebras |
| title_fullStr | Hom-structures and bihom-structures of antiflexible and pre-antiflexible algebras |
| title_full_unstemmed | Hom-structures and bihom-structures of antiflexible and pre-antiflexible algebras |
| title_short | Hom-structures and bihom-structures of antiflexible and pre-antiflexible algebras |
| title_sort | hom-structures and bihom-structures of antiflexible and pre-antiflexible algebras |
| topic_facet | anti-flexible algebras pre-anti-flexible algebras Rota-Baxter operators Nijenhuis operators anti-flexible algebras pre-anti-flexible algebras Rota-Baxter operators Nijenhuis operators |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/9598 |
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