| Title: | On certain functional equation related to derivations |
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| Authors: | ID Marcen, Benjamin (Author)
ID Vukman, Joso (Author) |
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| Files: |  https://www.degruyter.com/document/doi/10.1515/math-2023-0166/html
 On_certain_functional_Marcen_2024.pdf (2,67 MB)
MD5: 56DBDBFB4DD1D390B2C992E3390F6D5A
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| Language: | English |
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| Work type: | Scientific work |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | FL - Faculty of Logistic
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| Abstract: | In this article, we prove the following result. Let n ≥ 3 be some fixed integer and let R be a prime ring with ≠ + − char R n 1 !2n 2 ( ) ( ) . Suppose there exists an additive mapping D : R → R satisfying the relation 2n−2 D ( x n ) = ( n − 2 ∑ i = 0 ( n − 2 i ) x i D ( x 2 ) x n − 2 − i ) + ( 2 n − 2 − 1 ) ( D ( x ) x n − 1 + x n − 1 D ( x ) ) + n − 2 ∑ i = 1 ( i ∑ k = 2 ( 2 k − 1 − 1 ) ( n − k − 2 i − k ) + n − 1 − i ∑ k = 2 ( 2 k − 1 − 1 ) ( n − k − 2 n − i − k − 1 ) ) x i D ( x ) x n − 1 − i for all x ∈ R. In this case, D is a derivation. This result is related to a classical result of Herstein, which states that any Jordan derivation on a prime ring with char(R) ≠ 2 is a derivation. |
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| Keywords: | prime ring, semiprime ring, derivation, Jordan derivation, functional equation |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Submitted for review: | 04.02.2022 |
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| Article acceptance date: | 03.12.2023 |
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| Publication date: | 06.02.2024 |
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| Publisher: | De Gruyter Open |
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| Year of publishing: | 2024 |
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| Number of pages: | Str. 1-23 |
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| Numbering: | Letn. 22, št. 1 |
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| PID: | 20.500.12556/DKUM-93758  |
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| UDC: | 517.965 |
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| ISSN on article: | 2391-5455 |
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| COBISS.SI-ID: | 190231299 |
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| DOI: | 10.1515/math-2023-0166 |
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| Publication date in DKUM: | 18.07.2025 |
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| Views: | 258 |
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| Downloads: | 12 |
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| Metadata: |    |
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| Categories: | Misc.
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