Lie ideals in prime Γ-rings with derivations

• Autorzy: Nishteman N. Suliman , Abdul-Rahman H. Majeed
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

prime Γ-rings; Lie ideals; derivations

Kategorie tematyczne

• 16Y99: None of the above, but in this section
• 16N60: Prime and semiprime rings
• 16W25: Derivations, actions of Lie algebras

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2013
• Tom: 33
• Numer: 1
• Strony: 49-56

Daty

wydano

2013

otrzymano

2012-10-24

poprawiono

2013-01-03

Twórcy

autor

Nishteman N. Suliman

• Salahaddin University, Department of Mathematics, Erbil, Iraq

autor

Abdul-Rahman H. Majeed

• Baghdad University, Department of Mathematics, Baghdad, Iraq

Bibliografia

• [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.
• [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.
• [5] N. Nobusawa, On a Generlazetion of the Ring Theory, Osaka J. Math. 1 (1964) 81-89.
• [6] M. Soyturk, The Commutativity in Prime Gamma Rings with Derivation, Tr. J. Math. 18 (1994) 149-155.

Identyfikatory

DOI

10.7151/dmgaa.1199