TY  - JOUR
T1  - Some Commutativity Theorems on Lie Ideals of Semiprime Rings
TT  - Yarıasal Halkaların Lie İdealleri Üzerinde Bazı Değişmelilik Teoremleri
AU  - Bedir, Zeliha
AU  - Gölbaşı, Öznur
PY  - 2020
DA  - December
Y2  - 2020
DO  - 10.37094/adyujsci.638265
JF  - Adıyaman University Journal of Science
JO  - ADYU J SCI
PB  - Adıyaman University
WT  - DergiPark
SN  - 2147-1630
SP  - 548
EP  - 556
VL  - 10
IS  - 2
LA  - en
AB  - In this paper, we show that any 𝑈 noncentral square closed Lie ideal of a 2 −torsion free semiprime ring 𝑅 contains a nonzero ideal. With this result, some theorems will be extended on the multiplicative generalized derivations of Lie ideals of semiprime rings.
KW  - semiprime ring
KW  - Lie ideal
KW  - multiplicative generalized derivation
N2  - Bu çalışmada, 2 −torsion free bir 𝑅 yarıasal halkasının kare kapalı merkezi olmayan bir 𝑈 Lie idealinin, halkanın sıfırdan farklı bir idealini kapsadığı gösterilecektir. Ayrıca bu sonuçla, yarı asal halkaların Lie ideallerinin çarpımsal genelleştirilmiş türevleri üzerine bazı teoremler genelleştirilecektir.
CR  - [1] Bresar, M., On the distance of the composition of two derivations to be the generalized derivations, The Glasgow Mathematical Journal, 33, 89-93, 1991.
CR  - [2] Posner, E.C., Derivations in Prime Rings, Proceedings of the American Mathematical Society, 8, 1093-1100, 1957.
CR  - [3] Herstein, I.N., Topics in ring theory, University of Chicago Press, 1969.
CR  - [4] Martindale, W.S., When are multiplicative maps additive, Proceedings of the American Mathematical Society, 21, 695-698, 1969.
CR  - [5] Daif, M.N., When is a multiplicative derivation additive, International Journal of Mathematics and Mathematical Sciences, 14(3), 615-618, 1991.
CR  - [6] Goldman, H., Semrl, P ., Multiplicative derivations on C(X), Monatshefte für Mathematik, 121(3), 189-197, 1969.
CR  - [7] Daif, M. N., Tammam El-Sayiad, M.S., Multiplicative generalized derivations which are additive, East-West Journal of Mathematics, 9, 31-37, 1997.
CR  - [8] Dhara, B., Ali, S., On multiplicative (generalized)-derivation in prime and semiprime rings, Aequationes mathematicae, 86, 65-79, 2013.
CR  - [9] Eremita, D., Ilisevic, D., On additivity of centralizers, Bulletin of the Australian Mathematical Society, 74, 177-184, 2006.
CR  - [10] Ali, A., Dhara, B., Ali, F., Multiplicative (generalized)-derivations and left ideals in semiprime rings, Hacettepe Journal of Mathematics and Statistics, 44, 1293-1306, 2015.
CR  - [11] Ali, S., Dhara, B., Dar, N.A., Khan, A.N., On Lie ideals with multiplicative (generalized)-derivations in prime and semiprime rings, Beiträge zur Algebra und Geometrie, 56, 325-337, 2015.
CR  - [12] Koç, E., Gölbaşı, Ö., Multiplicative generalized derivations on Lie ideals in semiprime rings, Palastine Journal of Mathematics, 6, 219-227, 2017.
CR  - [13] Gölbaşı, Ö., Multiplicative generalized derivations on ideals in semiprime rings, Mathematica Slovaca, 66, 1285-1296, 2016.
CR  - [14] Huang, S., Derivations on Lie ideals of semiprime rings, Gulf Journal of Mathematics, 6(3), 25-32, 2018.
CR  - [15] Samman, M.S., Alyamani, N., Derivations on semiprime ring, International Journal of Pure and Applied Mathematics, 5(4), 469-477, 2003.
UR  - https://doi.org/10.37094/adyujsci.638265
L1  - https://dergipark.org.tr/en/download/article-file/840041
ER  -