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| Content Provider | Springer Nature Link |
|---|---|
| Author | Ali, Shakir |
| Copyright Year | 2011 |
| Abstract | The purpose of this paper is to establish some results concerning generalized left derivations in rings and Banach algebras. In fact, we prove the following results: Let R be a 2-torsion free semiprime ring, and let $${G: R \longrightarrow R}$$ be a generalized Jordan left derivation with associated Jordan left derivation $${\delta: R \longrightarrow R}$$ . Then every generalized Jordan left derivation is a generalized left derivation on R. This result gives an affirmative answer to the question posed as a remark in Ashraf and Ali (Bull. Korean Math. Soc. 45:253–261, 2008). Also, the study of generalized left derivation has been made which acts as a homomorphism or as an anti-homomorphism on some appropriate subset of the ring R. Further, we introduce the notion of generalized left bi-derivation and prove that if a prime ring R admits a generalized left bi-derivation G with associated left bi-derivation B then either R is commutative or G is a right bi-centralizer (or bi-multiplier) on R. Finally, it is shown that every generalized Jordan left derivation on a semisimple Banach algebra is continuous. |
| Ending Page | 226 |
| Page Count | 18 |
| Starting Page | 209 |
| File Format | |
| ISSN | 00019054 |
| e-ISSN | 14208903 |
| Journal | Aequationes mathematicae |
| Issue Number | 3 |
| Volume Number | 81 |
| Language | English |
| Publisher | SP Birkhäuser Verlag Basel |
| Publisher Date | 2011-04-19 |
| Publisher Place | Basel |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | semisimple Banach algebra generalized Jordan left (right) derivation Prime and semiprime rings Analysis Derivations, actions of Lie algebras Prime (semiprime) ring Commutators, derivations, elementary operators, etc. Combinatorics generalized left (right) derivation left (right) bi-derivation generalized left (right) bi-derivation and left (right) bi-centralizer (bi-multiplier) Hilbert algebras |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Discrete Mathematics and Combinatorics |
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