On Lie ideals and Jordan left derivations of prime rings

Mohammad Ashraf; Nadeem-ur-Rehman

Archivum Mathematicum (2000)

  • Volume: 036, Issue: 3, page 201-206
  • ISSN: 0044-8753

Abstract

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Let R be a 2-torsion free prime ring and let U be a Lie ideal of R such that u 2 ∈ U for all u ∈ U . In the present paper it is shown that if d is an additive mappings of R into itself satisfying d ( u 2 ) = 2 u d ( u ) for all u ∈ U , then d ( u v ) = u d ( v ) + v d ( u ) for all u , v ∈ U .

How to cite

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Ashraf, Mohammad, and Nadeem-ur-Rehman. "On Lie ideals and Jordan left derivations of prime rings." Archivum Mathematicum 036.3 (2000): 201-206. <http://eudml.org/doc/248559>.

@article{Ashraf2000,
abstract = {Let $R$ be a 2-torsion free prime ring and let $U$ be a Lie ideal of $R$ such that $u^\{2\} \in U$ for all $u \in U$. In the present paper it is shown that if $d$ is an additive mappings of $R$ into itself satisfying $d(u^\{2\})=2ud(u)$ for all $u \in U$, then $d(uv)=ud(v)+vd(u)$ for all $u,v \in U$.},
author = {Ashraf, Mohammad, Nadeem-ur-Rehman},
journal = {Archivum Mathematicum},
keywords = {Lie ideals; prime rings; Jordan left derivations; left derivations; torsion free rings; Lie ideals; prime rings; Jordan left derivations; additive mappings; torsion free rings},
language = {eng},
number = {3},
pages = {201-206},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On Lie ideals and Jordan left derivations of prime rings},
url = {http://eudml.org/doc/248559},
volume = {036},
year = {2000},
}

TY - JOUR
AU - Ashraf, Mohammad
AU - Nadeem-ur-Rehman
TI - On Lie ideals and Jordan left derivations of prime rings
JO - Archivum Mathematicum
PY - 2000
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 036
IS - 3
SP - 201
EP - 206
AB - Let $R$ be a 2-torsion free prime ring and let $U$ be a Lie ideal of $R$ such that $u^{2} \in U$ for all $u \in U$. In the present paper it is shown that if $d$ is an additive mappings of $R$ into itself satisfying $d(u^{2})=2ud(u)$ for all $u \in U$, then $d(uv)=ud(v)+vd(u)$ for all $u,v \in U$.
LA - eng
KW - Lie ideals; prime rings; Jordan left derivations; left derivations; torsion free rings; Lie ideals; prime rings; Jordan left derivations; additive mappings; torsion free rings
UR - http://eudml.org/doc/248559
ER -

References

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  1. Awtar R., Lie ideals and Jordan derivations of prime rings, Proc. Amer. Math. Soc. 90 (1984), 9–14. (1984) Zbl0528.16020MR0722405
  2. Bergen J., Herstein I. N., Ker J. W., Lie ideals and derivations of prime rings , J. Algebra 71 (1981), 259–267. (1981) MR0627439
  3. Bresar M., Jordan derivations on semiprime rings, Proc. Amer. Math. Soc. 104 (1988), 1003–1006. (1988) Zbl0691.16039MR0929422
  4. Bresar M., Vukman J., Jordan derivations of prime rings, Bull. Aust. Math. Soc. 37 (1988), 321–322. (1988) MR0943433
  5. Bresar M., Vukman J., On left derivations and related mappings, Proc. Amer. Math. Soc. 110 (1990), 7–16. (1990) Zbl0703.16020MR1028284
  6. Deng Q., On Jordan left derivations, Math. J. Okayama Univ. 34 (1992), 145–147. (1992) Zbl0813.16021MR1272614
  7. Herstein I. N., Jordan derivations of prime rings, Proc. Amer. Math. Soc. 8 (1957), 1104–1110. (1957) MR0095864
  8. Herstein I. N., Topics in ring theory, Univ. of Chcago Press, Chicago 1969. (1969) Zbl0232.16001MR0271135
  9. Kill-Wong Jun, Byung-Do Kim, A note on Jordan left derivations, Bull. Korean Math. Soc. 33 (1996) No. 2, 221–228. (1996) MR1405475
  10. Posner E. C., Derivations in prime rings, Proc. Amer. Math. Soc. 8 (1957), 1093–1100. (1957) MR0095863
  11. Vukman J., Jordan left derivations on semiprime rings, Math. J. Okayama Univ. (to appear). Zbl0937.16044MR1680747

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