Generalized Jordan N-Derivations of Unital Algebras with Idempotents
Let A be a unital algebra with idempotent e over a 2-torsionfree unital commutative ring ℛ and S:A⟶A be an arbitrary generalized Jordan n-derivation associated with a Jordan n-derivation J. We show that, under mild conditions, every generalized Jordan n-derivation S:A⟶A is of the form Sx=λx+Jx in th...
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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/10.1155/2021/9997646 |
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| _version_ | 1832546089721397248 |
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| author | Xinfeng Liang |
| author_facet | Xinfeng Liang |
| author_sort | Xinfeng Liang |
| collection | DOAJ |
| description | Let A be a unital algebra with idempotent e over a 2-torsionfree unital commutative ring ℛ and S:A⟶A be an arbitrary generalized Jordan n-derivation associated with a Jordan n-derivation J. We show that, under mild conditions, every generalized Jordan n-derivation S:A⟶A is of the form Sx=λx+Jx in the current work. As an application, we give a description of generalized Jordan derivations for the condition n=2 on classical examples of unital algebras with idempotents: triangular algebras, matrix algebras, nest algebras, and algebras of all bounded linear operators, which generalize some known results. |
| format | Article |
| id | doaj-art-d54c108e74894690889893c21f54eca5 |
| 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-d54c108e74894690889893c21f54eca52025-02-03T07:23:54ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/99976469997646Generalized Jordan N-Derivations of Unital Algebras with IdempotentsXinfeng Liang0School of Mathematics and Big Data, Anhui University of Science & Technology, Huainan 232001, ChinaLet A be a unital algebra with idempotent e over a 2-torsionfree unital commutative ring ℛ and S:A⟶A be an arbitrary generalized Jordan n-derivation associated with a Jordan n-derivation J. We show that, under mild conditions, every generalized Jordan n-derivation S:A⟶A is of the form Sx=λx+Jx in the current work. As an application, we give a description of generalized Jordan derivations for the condition n=2 on classical examples of unital algebras with idempotents: triangular algebras, matrix algebras, nest algebras, and algebras of all bounded linear operators, which generalize some known results.http://dx.doi.org/10.1155/2021/9997646 |
| spellingShingle | Xinfeng Liang Generalized Jordan N-Derivations of Unital Algebras with Idempotents Journal of Mathematics |
| title | Generalized Jordan N-Derivations of Unital Algebras with Idempotents |
| title_full | Generalized Jordan N-Derivations of Unital Algebras with Idempotents |
| title_fullStr | Generalized Jordan N-Derivations of Unital Algebras with Idempotents |
| title_full_unstemmed | Generalized Jordan N-Derivations of Unital Algebras with Idempotents |
| title_short | Generalized Jordan N-Derivations of Unital Algebras with Idempotents |
| title_sort | generalized jordan n derivations of unital algebras with idempotents |
| url | http://dx.doi.org/10.1155/2021/9997646 |
| work_keys_str_mv | AT xinfengliang generalizedjordannderivationsofunitalalgebraswithidempotents |