On (m,n)-Derivations of Some Algebras
Let A be a unital algebra, δ be a linear mapping from A into itself and m, n be fixed integers. We call δ an (m, n)-derivable mapping at Z, if mδ(AB) + nδ(BA) = mδ(A)B + mAδ(B) + nδ(B)A for all A,B ∈ A with AB = Z. In this paper, (m, n)-derivable mappings at 0 (resp. IA ⊕ 0, I) on generalized matrix...
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| Format: | Article |
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De Gruyter
2014-07-01
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| Series: | Demonstratio Mathematica |
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| Online Access: | http://www.degruyter.com/view/j/dema.2014.47.issue-3/dema-2014-0054/dema-2014-0054.xml?format=INT |
| _version_ | 1818368661082079232 |
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| author | Shen Qihua Li Jiankui Guo Jianbin |
| author_facet | Shen Qihua Li Jiankui Guo Jianbin |
| author_sort | Shen Qihua |
| collection | DOAJ |
| description | Let A be a unital algebra, δ be a linear mapping from A into itself and m, n be fixed integers. We call δ an (m, n)-derivable mapping at Z, if mδ(AB) + nδ(BA) = mδ(A)B + mAδ(B) + nδ(B)A for all A,B ∈ A with AB = Z. In this paper, (m, n)-derivable mappings at 0 (resp. IA ⊕ 0, I) on generalized matrix algebras are characterized. We also study (m, n)-derivable mappings at 0 on CSL algebras. We reveal the relationship between this kind of mappings with Lie derivations, Jordan derivations and derivations. |
| first_indexed | 2024-12-13T23:11:29Z |
| format | Article |
| id | doaj.art-aed567b3336441a2bffe4f9c15708244 |
| institution | Directory Open Access Journal |
| issn | 0420-1213 2391-4661 |
| language | English |
| last_indexed | 2024-12-13T23:11:29Z |
| publishDate | 2014-07-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Demonstratio Mathematica |
| spelling | doaj.art-aed567b3336441a2bffe4f9c157082442022-12-21T23:28:06ZengDe GruyterDemonstratio Mathematica0420-12132391-46612014-07-0147367269410.2478/dema-2014-0054dema-2014-0054On (m,n)-Derivations of Some AlgebrasShen Qihua0Li Jiankui1Guo Jianbin2SCHOOL OF MATHEMATICS AND INFORMATION SHANGHAI LIXIN UNIVERSITY OF COMMERCE SHANGHAI, 201620, PR CHINADEPARTMENT OF MATHEMATICS EAST CHINA UNIVERSITY OF SCIENCE AND TECHNOLOGY SHANGHAI 200237, PR CHINADEPARTMENT OF MATHEMATICS EAST CHINA UNIVERSITY OF SCIENCE AND TECHNOLOGY SHANGHAI 200237, PR CHINALet A be a unital algebra, δ be a linear mapping from A into itself and m, n be fixed integers. We call δ an (m, n)-derivable mapping at Z, if mδ(AB) + nδ(BA) = mδ(A)B + mAδ(B) + nδ(B)A for all A,B ∈ A with AB = Z. In this paper, (m, n)-derivable mappings at 0 (resp. IA ⊕ 0, I) on generalized matrix algebras are characterized. We also study (m, n)-derivable mappings at 0 on CSL algebras. We reveal the relationship between this kind of mappings with Lie derivations, Jordan derivations and derivations.http://www.degruyter.com/view/j/dema.2014.47.issue-3/dema-2014-0054/dema-2014-0054.xml?format=INTand phrases: CSL algebraderivationgeneralized matrix algebra(m,n)- derivation |
| spellingShingle | Shen Qihua Li Jiankui Guo Jianbin On (m,n)-Derivations of Some Algebras Demonstratio Mathematica and phrases: CSL algebra derivation generalized matrix algebra (m,n)- derivation |
| title | On (m,n)-Derivations of Some Algebras |
| title_full | On (m,n)-Derivations of Some Algebras |
| title_fullStr | On (m,n)-Derivations of Some Algebras |
| title_full_unstemmed | On (m,n)-Derivations of Some Algebras |
| title_short | On (m,n)-Derivations of Some Algebras |
| title_sort | on m n derivations of some algebras |
| topic | and phrases: CSL algebra derivation generalized matrix algebra (m,n)- derivation |
| url | http://www.degruyter.com/view/j/dema.2014.47.issue-3/dema-2014-0054/dema-2014-0054.xml?format=INT |
| work_keys_str_mv | AT shenqihua onmnderivationsofsomealgebras AT lijiankui onmnderivationsofsomealgebras AT guojianbin onmnderivationsofsomealgebras |