σ- ideals and generalized derivations in σ-prime rings
Let R be a prime ring and F and G be generalized derivations of R with associated derivations d and g respectively. In the present paper, we shall investigate the commutativity of R admitting generalized derivations F and G satisfying any one of the properties: (i) F(x)x = x G(x), (ii) F(x2) = x2 ,...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Sociedade Brasileira de Matemática
2013-12-01
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| Series: | Boletim da Sociedade Paranaense de Matemática |
| Subjects: | |
| Online Access: | http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/12119 |
| _version_ | 1818900392275083264 |
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| author | M. Rais Khan Deepa Arora M. Ali Khan |
| author_facet | M. Rais Khan Deepa Arora M. Ali Khan |
| author_sort | M. Rais Khan |
| collection | DOAJ |
| description | Let R be a prime ring and F and G be generalized derivations of R with associated derivations d and g respectively. In the present paper, we shall investigate the commutativity of R admitting generalized derivations F and G satisfying any one of the properties: (i) F(x)x = x G(x), (ii) F(x2) = x2 , (iii) [F(x), y] = [x, G(y)], (iv) d(x)F(y) = xy, (v) F([x, y]) = [F(x), y] + [d(y), x] and (vi) F(x ◦ y) = F(x) ◦ y − d(y) ◦ x for all x, y in some appropriate subset of R. |
| first_indexed | 2024-12-19T20:03:08Z |
| format | Article |
| id | doaj.art-567f9448c97b4f419008a90511a8d633 |
| institution | Directory Open Access Journal |
| issn | 0037-8712 2175-1188 |
| language | English |
| last_indexed | 2024-12-19T20:03:08Z |
| publishDate | 2013-12-01 |
| publisher | Sociedade Brasileira de Matemática |
| record_format | Article |
| series | Boletim da Sociedade Paranaense de Matemática |
| spelling | doaj.art-567f9448c97b4f419008a90511a8d6332022-12-21T20:07:35ZengSociedade Brasileira de MatemáticaBoletim da Sociedade Paranaense de Matemática0037-87122175-11882013-12-0131211311910.5269/bspm.v31i2.121198084σ- ideals and generalized derivations in σ-prime ringsM. Rais Khan0Deepa Arora1M. Ali Khan2JamiaMilliaIslamia (Central University) Department of MathematicsJamiaMilliaIslamia (Central University) Department of MathematicsJamiaMilliaIslamia (Central University) Department of MathematicsLet R be a prime ring and F and G be generalized derivations of R with associated derivations d and g respectively. In the present paper, we shall investigate the commutativity of R admitting generalized derivations F and G satisfying any one of the properties: (i) F(x)x = x G(x), (ii) F(x2) = x2 , (iii) [F(x), y] = [x, G(y)], (iv) d(x)F(y) = xy, (v) F([x, y]) = [F(x), y] + [d(y), x] and (vi) F(x ◦ y) = F(x) ◦ y − d(y) ◦ x for all x, y in some appropriate subset of R.http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/12119Generalized derivationsσ-idealsrings with involutionσ-prime rings |
| spellingShingle | M. Rais Khan Deepa Arora M. Ali Khan σ- ideals and generalized derivations in σ-prime rings Boletim da Sociedade Paranaense de Matemática Generalized derivations σ-ideals rings with involution σ-prime rings |
| title | σ- ideals and generalized derivations in σ-prime rings |
| title_full | σ- ideals and generalized derivations in σ-prime rings |
| title_fullStr | σ- ideals and generalized derivations in σ-prime rings |
| title_full_unstemmed | σ- ideals and generalized derivations in σ-prime rings |
| title_short | σ- ideals and generalized derivations in σ-prime rings |
| title_sort | σ ideals and generalized derivations in σ prime rings |
| topic | Generalized derivations σ-ideals rings with involution σ-prime rings |
| url | http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/12119 |
| work_keys_str_mv | AT mraiskhan sidealsandgeneralizedderivationsinsprimerings AT deepaarora sidealsandgeneralizedderivationsinsprimerings AT malikhan sidealsandgeneralizedderivationsinsprimerings |