Derivations satisfying certain algebraic identities on Lie ideals
Let d be a derivation of a semiprime ring R and L a nonzero Lie ideal of R. In this note, it is proved that every noncentral square-closed Lie ideal of R contains a nonzero ideal of R. Further, we use this result to characterize the conditions: d(xy) = d(x)d(y), d(xy) = d(y)d(x) on L. With this, a t...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Kragujevac, Faculty of Technical Sciences Čačak, Serbia
2019-01-01
|
| Series: | Mathematica Moravica |
| Subjects: | |
| Online Access: | https://scindeks-clanci.ceon.rs/data/pdf/1450-5932/2019/1450-59321902079S.pdf |
| id |
doaj-0a8dde2c5e434d128ed862e57fd5c24a |
|---|---|
| record_format |
Article |
| spelling |
doaj-0a8dde2c5e434d128ed862e57fd5c24a2020-11-25T04:09:13ZengUniversity of Kragujevac, Faculty of Technical Sciences Čačak, SerbiaMathematica Moravica1450-59322560-55422019-01-0123279861450-59321902079SDerivations satisfying certain algebraic identities on Lie idealsSandhu Gurninder S.0Kumar Deepak1Patel Memorial National College, Department of Mathematics, Rajpura, Punjab, IndiaPunjabi University, Department of Mathematics, Patiala, Punjab, IndiaLet d be a derivation of a semiprime ring R and L a nonzero Lie ideal of R. In this note, it is proved that every noncentral square-closed Lie ideal of R contains a nonzero ideal of R. Further, we use this result to characterize the conditions: d(xy) = d(x)d(y), d(xy) = d(y)d(x) on L. With this, a theorem of Ali et al. [14] can be deduced.https://scindeks-clanci.ceon.rs/data/pdf/1450-5932/2019/1450-59321902079S.pdfsemiprime ringlie idealsderivation |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Sandhu Gurninder S. Kumar Deepak |
| spellingShingle |
Sandhu Gurninder S. Kumar Deepak Derivations satisfying certain algebraic identities on Lie ideals Mathematica Moravica semiprime ring lie ideals derivation |
| author_facet |
Sandhu Gurninder S. Kumar Deepak |
| author_sort |
Sandhu Gurninder S. |
| title |
Derivations satisfying certain algebraic identities on Lie ideals |
| title_short |
Derivations satisfying certain algebraic identities on Lie ideals |
| title_full |
Derivations satisfying certain algebraic identities on Lie ideals |
| title_fullStr |
Derivations satisfying certain algebraic identities on Lie ideals |
| title_full_unstemmed |
Derivations satisfying certain algebraic identities on Lie ideals |
| title_sort |
derivations satisfying certain algebraic identities on lie ideals |
| publisher |
University of Kragujevac, Faculty of Technical Sciences Čačak, Serbia |
| series |
Mathematica Moravica |
| issn |
1450-5932 2560-5542 |
| publishDate |
2019-01-01 |
| description |
Let d be a derivation of a semiprime ring R and L a nonzero Lie ideal of R. In this note, it is proved that every noncentral square-closed Lie ideal of R contains a nonzero ideal of R. Further, we use this result to characterize the conditions: d(xy) = d(x)d(y), d(xy) = d(y)d(x) on L. With this, a theorem of Ali et al. [14] can be deduced. |
| topic |
semiprime ring lie ideals derivation |
| url |
https://scindeks-clanci.ceon.rs/data/pdf/1450-5932/2019/1450-59321902079S.pdf |
| work_keys_str_mv |
AT sandhugurninders derivationssatisfyingcertainalgebraicidentitiesonlieideals AT kumardeepak derivationssatisfyingcertainalgebraicidentitiesonlieideals |
| _version_ |
1724422794912989184 |