# Lie ideals in prime Γ-rings with derivations

Nishteman N. Suliman; Abdul-Rahman H. Majeed

Discussiones Mathematicae - General Algebra and Applications (2013)

- Volume: 33, Issue: 1, page 49-56
- ISSN: 1509-9415

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topNishteman N. Suliman, and Abdul-Rahman H. Majeed. "Lie ideals in prime Γ-rings with derivations." Discussiones Mathematicae - General Algebra and Applications 33.1 (2013): 49-56. <http://eudml.org/doc/270176>.

@article{NishtemanN2013,

abstract = {
Let M be a 2 and 3-torsion free prime Γ-ring, d a nonzero derivation on M and U a nonzero Lie ideal of M. In this paper it is proved that U is a central Lie ideal of M if d satisfies one of the following
(i) d(U)⊂ Z,
(ii) d(U)⊂ U and d²(U)=0,
(iii) d(U)⊂ U, d²(U)⊂ Z.
},

author = {Nishteman N. Suliman, Abdul-Rahman H. Majeed},

journal = {Discussiones Mathematicae - General Algebra and Applications},

keywords = {prime Γ-rings; Lie ideals; derivations; prime -rings; central Lie ideals},

language = {eng},

number = {1},

pages = {49-56},

title = {Lie ideals in prime Γ-rings with derivations},

url = {http://eudml.org/doc/270176},

volume = {33},

year = {2013},

}

TY - JOUR

AU - Nishteman N. Suliman

AU - Abdul-Rahman H. Majeed

TI - Lie ideals in prime Γ-rings with derivations

JO - Discussiones Mathematicae - General Algebra and Applications

PY - 2013

VL - 33

IS - 1

SP - 49

EP - 56

AB -
Let M be a 2 and 3-torsion free prime Γ-ring, d a nonzero derivation on M and U a nonzero Lie ideal of M. In this paper it is proved that U is a central Lie ideal of M if d satisfies one of the following
(i) d(U)⊂ Z,
(ii) d(U)⊂ U and d²(U)=0,
(iii) d(U)⊂ U, d²(U)⊂ Z.

LA - eng

KW - prime Γ-rings; Lie ideals; derivations; prime -rings; central Lie ideals

UR - http://eudml.org/doc/270176

ER -

## References

top- [1] W. E. Barness, On the Γ-Rings of Nobusawa, Pacific J. Math. 18 (1966) 411-422. doi: 10.2140/pjm.1966.18.411.
- [2] J. Bergan, I. N. Herstein, and W. Kerr, Lie Ideals and Derivations of Prime Rings, J. Algebra 71 (1981) 259-267. doi: 10.1016/0021-8693(81)90120-4. Zbl0463.16023
- [3] A. K. Halder and A. C. Paul, Jordan Left Derivations on Lie Ideals of Prime Γ-Rings, Punjab Univ. J. of Math. (2011) 1-7.
- [4] P.H.Lee and T.K.Lee, Lie Ideals of Prime Rings with Derivations, Bull. Inst. Math. Acad. Scin. 11 (1983) 75-80. Zbl0515.16018
- [5] N. Nobusawa, On a Generlazetion of the Ring Theory, Osaka J. Math. 1 (1964) 81-89. Zbl0135.02701
- [6] M. Soyturk, The Commutativity in Prime Gamma Rings with Derivation, Tr. J. Math. 18 (1994) 149-155. Zbl0860.16039

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