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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 2314-4629 2314-4785 |